a tensor artificial viscosity using a mimetic finite difference algorithm abstract we have developed a two dimensional tensor artificial viscosity for finite difference shock wave computations the discrete viscosity tensor is formed by multiplying the gradient of velocity tensor by a scalar term the scalar term is based on the form of viscosity first presented by kurapatanko and also contains a limiter designed to switch off the viscosity for shockless compression and rigid body rotation mimetic discretizations are used to derive the form of the momentum and energy equations for a nonorthogonal grid where the viscosity tensor is evaluated at the zone edges the advantage of the tensor viscosity is a reduction of the dependence of the solution on the relation of the grid to the flow structure

a low diffusive lagrange remap scheme for the simulation of violent air water free surface flows in 2002 despres and lagoutiere 17 proposed a low diffusive advection scheme for pure transport equation problems which is particularly accurate for step shaped solutions and thus suited for interface tracking procedure by a color function this has been extended by kokh and lagoutiere 28 in the context of compressible multifluid flows using a five equation model in this paper we explore a simplified variant approach for gas liquid three equation models the eulerian numerical scheme has two ingredients a robust remapped lagrange solver for the solution of the volume averaged equations and a low diffusive compressive scheme for the advection of the gas mass fraction numerical experiments show the performance of the computational approach on various flow reference problems dam break sloshing of a tank filled with water water water impact and finally a case of rayleigh taylor instability one of the advantages of the present interface capturing solver is its natural implementation on parallel processors or computers

coupling an eulerian fluid calculation to a lagrangian solid calculation with the ghost fluid method we propose a numerical method for modeling multimaterial flows where the domain is decomposed into separate eulerian and lagrangian subdomains that is the equations are written in eulerian form in one subdomain and in lagrangian form in the other subdomain this is of interest for example when considering the effect of underwater explosions on the hull of a ship or the impact of a low speed projectile on a soft explosive target on the one hand high speed fluid flows are traditionally modeled by applying shock capturing schemes to the compressible euler equations to avoid problems associated with tangling of a lagrangian mesh on the other hand solid dynamics calculations are traditionally carried out using lagrangian numerical methods to avoid problems associated with numerical smearing in eulerian calculations we use the ghost fluid method to create accurate discretizations across the eulerian lagrangian interface the numerical method is presented in both one and two spatial dimensions three dimensional extensions to the interface coupling method are straightforward

a 3d lagrangian cell centered hydrodynamic method with higher order reconstructions for gas and solid dynamics abstract the lagrangian finite volume cell centered hydrodynamic method introduces dissipation into the calculation by solving a multidirectional approximate riemann problem the amount of dissipation created is a function of the jump in the velocity and stress at the node these jumps in velocity and stress can be reduced by using higher order reconstructions that are constructed by fitting cell average values in neighboring cells one challenge is that a large stencil is required to create high order reconstructions to address this challenge a new two step reconstruction process is proposed to build a quadratic polynomial by only communicating with face neighboring cells the two step reconstruction method is applied to scalar vector and tensor fields another challenge is that limiters must be used to reduce the higher order reconstructions towards piecewise constant fields near discontinuities to prevent artificial new extrema we address this second challenge and propose a new hierarchical limiter that uses a discrete mach number as a smoothness indicator the inclusion of the mach number is essential for minimizing dissipation errors the new limiter is used with the reconstructions of pressure velocity and deviatoric stress the accuracy and robustness of the new two step reconstruction method with the new limiter is demonstrated by simulating a suite of 3d cartesian test problems covering both gas and solid dynamics

moment of fluid interface reconstruction method in multi material arbitrary lagrangian eulerian mmale algorithms a new lagrangian interface evolution method to use in a multi material ale mmale algorithm is proposed the input data set for the method consists of the volume fractions after the lagrangian step and the orientation position of the interfaces before this step in the present work the moment of fluid mof method is used at the end of the ale cycle to provide required interface information for this method compared to traditional reconstruction methods in addition to the volume fractions the proposed method incorporates the configuration of the interfaces in the calculations the effect of compressibility is also considered in prioritizing the materials the capability of the method is assessed by testing its potential to track interfaces through large topology change in the domains which contain two or more materials numerical results for these tough test problems provide enough evidence for the accuracy and robustness of the proposed method

a robust and efficient polyhedron subdivision and intersection algorithm for three dimensional mmale remapping the multi material arbitrary lagrangian eulerian mmale method is an effective way to simulate the multi material flow with severe surface deformation comparing with the traditional arbitrary lagrangian eulerian ale method the mmale method allows for multiple materials in a single cell which overcomes the difficulties in grid refinement process in recent decades many researches have been conducted for the lagrangian rezoning and surface reconstruction phases but less attention has been paid to the multi material remapping phase especially for the three dimensional problems due to two complex geometric problems the polyhedron subdivision and the polyhedron intersection in this paper we propose a clipping and projecting algorithm for polyhedron intersection whose basic idea comes from the commonly used method by grandy 1999 29 and jia et al 2013 34 our new algorithm solves the geometric problem by an incremental modification of the topology based on segmentplane intersections a comparison with jia et al 2013 34 shows our new method improves the efficiency by 55 to 65 when calculating polyhedron intersections moreover the instability caused by the geometric degeneracy can be thoroughly avoided because the geometry integrity is preserved in the new algorithm we also focus on the polyhedron subdivision process and describe an algorithm which could automatically and precisely tackle the various situations including convex non convex and multiple subdivisions numerical studies indicate that by using our polyhedron subdivision and intersection algorithm the volume conversation of the remapping phase can be exactly preserved in the mmale simulation

blind source separation in the time frequency domain based on multiple hypothesis testing this paper considers a time frequency t f based approach for blind separation of nonstationary signals in particular we propose a time frequency point selection algorithm based on multiple hypothesis testing which allows automatic selection of auto or cross source locations in the time frequency plane the selected t f points are then used via a joint diagonalization and off diagonalization algorithm to perform source separation the proposed algorithm is developed assuming deterministic signals with additive white complex gaussian noise a performance comparison of the proposed and existing approaches is provided

multi scale lagrangian shock hydrodynamics on q1 p0 finite elements theoretical framework and two dimensional computations abstract a new multi scale stabilized method for q1 p0 finite element computations of lagrangian shock hydrodynamics is presented instabilities of hourglass type are controlled by a stabilizing operator derived using the variational multi scale analysis paradigm the resulting stabilizing term takes the form of a pressure correction with respect to broadly accepted hourglass control approaches the novelty of the method resides in its residual based character the stabilizing residual has a definite physical significance since it embeds a discrete form of the clausius duhem inequality effectively the proposed stabilization samples the production of entropy to counter numerical instabilities the proposed technique is applied to materials with no shear strength e g fluids for which there exists a caloric equation of state and extensions to the case of materials with shear strength e g solids are also envisioned the stabilization operator is incorporated into a mid point predictor multi corrector time integration algorithm which conserves mass momentum and total energy encouraging numerical results in the context of compressible gas dynamics confirm the potential of the method

a free lagrange augmented godunov method for the simulation of elastic plastic solids a lagrangian finite volume godunov scheme is extended to simulate two dimensional solids in planar geometry the scheme employs an elastic perfectly plastic material model implemented using the method of radial return and either the stiffened gas or osborne equation of state to describe the material the problem of mesh entanglement common to conventional two dimensional lagrangian schemes is avoided by utilising the free lagrange method the lagrangian formulation enables features convecting at the local velocity such as material interfaces to be resolved with minimal numerical dissipation the governing equations are split into separate subproblems and solved sequentially in time using a time operator split procedure local riemann problems are solved using a two shock approximate riemann solver and piecewise linear data reconstruction is employed using a muscl based approach to improve spatial accuracy to illustrate the effectiveness of the technique numerical simulations are presented and compared with results from commercial fixed connectivity lagrangian and smooth particle hydrodynamics solvers autodyn 2d the simulations comprise the low velocity impact of an aluminium projectile on a semi infinite target the collapse of a thick walled beryllium cylinder and the high velocity impact of cylindrical aluminium and steel projectiles on a thin aluminium target the analytical solution for the collapse of a thick walled cylinder is also presented for comparison

using a curvilinear grid to construct symmetry preserving discretizations for lagrangian gas dynamics the goal of this paper is to construct discretizations for the equations of lagrangian gas dynamics that preserve plane cylindrical and spherical symmetry in the solution of the original differential equations the new method uses a curvilinear grid that is reconstructed from a given logically rectangular distribution of nodes the sides of the cells of the reconstructed grid can be segments of straight lines or arcs of local circles our procedure is exact for straight lines and circles that is it reproduces rectangular and polar grids exactly we use the method of support operators to construct a conservative finite difference method that we demonstrate will preserve spatial symmetries for certain choices of the initial grid we also introduce a curvilinear version of artificial edge viscosity that also preserves symmetry we present numerical examples to demonstrate our theoretical considerations and the robustness of the new method

on preservation of symmetry in r z staggered lagrangian schemes in the focus of this work are symmetry preservation conservation of energy and volume and other important properties of staggered lagrangian hydrodynamic schemes in cylindrical r z geometry it is well known that on quadrilateral cells in r z preservation of spherical symmetry perfect satisfaction of the geometrical conservation law gcl and total energy conservation are incompatible even on conforming grids this paper suggests a novel staggered grid approach that preserves symmetry conserves total energy by construction and tries to do its best by diminishing the gcl error to the order of entropy error in particular the forces from an existing volume consistent scheme are corrected so that spherical symmetry is preserved the incorporation of subcell pressure mechanism to reduce spurious grid deformations is described and the relation of the new scheme to popular area weighted and control volume approaches studied

bootstrap modeling of a class of nonstationary signals the problem of modeling polynomial phase signals is considered techniques based on the bootstrap and multiple hypotheses tests for optimal model selection of constant amplitude polynomial phase signals embedded in stationary noise are developed phase parameter estimators based on both the least squares method and the polynomial phase transform are used the proposed techniques are compared with existing ones including akaike s 1978 1974 information criterion and rissanen s 1978 minimum description length criterion and are shown to outperform these procedures for the considered small sample sizes

a framework for developing a mimetic tensor artificial viscosity for lagrangian hydrocodes on arbitrary polygonal meshes we construct a new mimetic tensor artificial viscosity on general polygonal meshes the tensor artificial viscosity is based on discretization of coordinate invariant operators divergence of a tensor and gradient of a vector the focus of this paper is on the non symmetric form div email protected u of the tensor artificial viscosity the discretizations of this operator is derived for the case of a full tensor coefficient m however in the numerical experiments we only use scalar m we prove that the new tensor viscosity preserves spatial symmetry on special meshes we demonstrate performance of the new viscosity for the noh implosion sedov explosion and saltzman piston problems on a set of various polygonal meshes in both cartesian and axisymmetric coordinate systems

parameter estimation for locally linear fm signals using a time frequency hough transform an estimator for the phase parameters of mono and multicomponent fm signals with both good numerical properties and statistical performance is proposed the proposed approach is based on the hough transform of the pseudo wigner ville time frequency distribution pwvd it is shown that the numerical properties of the estimator can be improved by varying the pwvd window length the effect of the window time extent on the statistical performance of the estimator is delineated experimental data is used for validation of the statistical properties

metric based mesh adaptation for 2d lagrangian compressible flows in this paper we present a method to compute compressible flows in 2d it uses two steps a lagrangian step and a metric based triangular mesh adaptation step computational mesh is locally adapted according to some metric field that depends on physical or geometrical data this mesh adaptation step embeds a conservative remapping procedure to satisfy consistency with euler equations the whole method is no more lagrangian after describing mesh adaptation patterns we recall the metric formalism then we detail an appropriate remapping procedure which is first order and relies on exact intersections we give some hints about the parallel implementation finally we present various numerical experiments which demonstrate the good properties of the algorithm

the construction of compatible hydrodynamics algorithms utilizing conservation of total energy the principal goal of all numerical algorithms is to represent as faithfully and accurately as possible the underlying continuum equations to which a numerical solution is sought however in the transformation of the equations of fluid dynamics into discretized form important physical properties are either lost or obeyed only to an approximation that often becomes worse with time this is because the numerical methods used to form the discrete analog of these equations may only represent them to some order of local truncation error without explicit regard to global properties of the continuum system although a finite truncation error is inherent to all discretization methods it is possible to satisfy certain global properties such as conservation of mass momentum and total energy to numerical roundoff error the purpose of this work is to show how these equations can be differenced compatibly so that they obey the aforementioned properties in particular it is shown how conservation of total energy can be utilized as an intermediate device to achieve this goal for the equations of fluid dynamics written in lagrangian form and with a staggered spatial placement of variables for any number of dimensions and in any coordinate system for staggered spatial variables it is shown how the momentum equation and the specific internal energy equation can be derived from each other in a simple and generic manner by use of the conservation of total energy this allows for the specification of forces that can be of an arbitrary complexity such as those derived from an artificial viscosity or subzonal pressures these forces originate only in discrete form nonetheless the change in internal energy caused by them is still completely determined the procedure given here is compared to the method of support operators to which it is closely related difficulties with conservation of momentum volume and entropy are also discussed the proper treatment of boundary conditions and differencing with respect to time are detailed

the internal consistency stability and accuracy of the discrete compatible formulation of lagrangian hydrodynamics this work explores the somewhat subtle meaning and consequences of the salient properties of the discrete compatible formulation of lagrangian hydrodynamics in particular since this formulation preserves total energy to roundoff error the amount of error in the conservation of total energy cannot be used to gauge the internal consistency of calculations as is often done with the older forms of this algorithm however the compatible formulation utilizes two definitions of zone volume the first is the usual definition whereby the volume of a zone is defined as some prescribed function of the coordinates of the points that define it the second is given as the integration in time of the continuity equation for zone volume as expressed in lagrangian form it is the use of this latter volume in the specific internal energy equation that enables total energy to be exactly conserved these two volume definitions are generally not precisely equal it is the analysis of this difference that forms the first part of this study it is shown that this difference in zone volumes can be used to construct a practical internal consistency measure that not only takes the place of the lack of total energy conservation of the older forms of lagrangian hydrodynamics but is more general in that it can be defined on a single zone basis it can also be used to ascertain the underlying spatial and temporal order of accuracy of any given set of calculations the difference in these two definitions of zone volume may be interpreted as a type of entropy error however this entropy error is found to be significant only when a given calculation becomes numerically unstable otherwise it remains at or far beneath truncation error levels in fact it can be utilized to provide an upper bound on the size of the spatial truncation error for a stable computation it is also shown how this volume difference can be used as an indicator of numerical difficulties since exact local conservation of total energy does not guarantee numerical stability or the quality of any numerical calculation the discrete compatible formulation of lagrangian hydrodynamics utilizes a two level predictor corrector type of time integration scheme a stability analysis both analytical and numerical is given this analysis reveals a novel stability diagram that has not been heretofore published and gives definitive information as to how the stabilizing corrector step should be centered in time

short note volume consistency in a staggered grid lagrangian hydrodynamics scheme staggered grid lagrangian schemes for compressible hydrodynamics involve a choice of how internal energy is advanced in time the options depend on two ways of defining cell volumes an indirect one that guarantees total energy conservation and a direct one that computes the volume from its definition as a function of the cell vertices it is shown that the motion of the vertices can be defined so that the two volume definitions are identical a so modified total energy conserving staggered scheme is applied to the coggeshall adiabatic compression problem and now also entropy is basically exactly conserved for each lagrangian cell and there is increased accuracy for internal energy the overall improvement as the grid is refined is less than what might be expected

blind separation of speech mixtures via time frequency masking binary time frequency masks are powerful tools for the separation of sources from a single mixture perfect demixing via binary time frequency masks is possible provided the time frequency representations of the sources do not overlap a condition we call w disjoint orthogonality we introduce here the concept of approximate w disjoint orthogonality and present experimental results demonstrating the level of approximate w disjoint orthogonality of speech in mixtures of various orders the results demonstrate that there exist ideal binary time frequency masks that can separate several speech signals from one mixture while determining these masks blindly from just one mixture is an open problem we show that we can approximate the ideal masks in the case where two anechoic mixtures are provided motivated by the maximum likelihood mixing parameter estimators we define a power weighted two dimensional 2 d histogram constructed from the ratio of the time frequency representations of the mixtures that is shown to have one peak for each source with peak location corresponding to the relative attenuation and delay mixing parameters the histogram is used to create time frequency masks that partition one of the mixtures into the original sources experimental results on speech mixtures verify the technique example demixing results can be found online at http alum mit edu www rickard bss html

entropy viscosity method for the single material euler equations in lagrangian frame a new finite element method for solving the euler equations in lagrangian coordinates is proposed the method is stabilized by adding artificial diffusion terms compatible with positivity of mass and internal energy a minimum principle on the specific entropy and all generalized entropy inequalities two options of first order artificial diffusion are considered one is in the spirit of the eulerian based method guermond et al 2011 23 22 zingan et al 2013 and the other is similar to existing viscosity stabilizations in lagrangian frame e g dobrev et al 2012 the method is verified to be high order for smooth solutions even with active viscosity terms this is achieved by using high order finite element spaces and an entropy based viscosity stabilization that degenerates the first order viscous terms this stabilization automatically distinguishes smooth and singular regions the formal accuracy and convergence properties of the proposed methods are tested on a series of benchmark problems this is the first result extending the entropy viscosity methodology to the lagrangian hydrodynamics

energy preservation and entropy in lagrangian space and time staggered hydrodynamic schemes usual space and time staggered sts leap frog lagrangian hydrodynamic schemes such as von neumann richtmyer s 1950 wilkins 1964 and their variants are widely used for their simplicity and robustness despite their known lack of exact energy conservation since the seminal work of trulio and trigger 1950 and despite the later corrections of burton 1991 it is generally accepted that these schemes cannot be modified to exactly conserve energy while retaining all of the following properties sts stencil with velocities half time centered with respect to positions explicit second order algorithm locally implicit for internal energy and definite positive kinetic energy it is shown here that it is actually possible to modify the usual sts hydrodynamic schemes in order to be exactly energy preserving regardless of the evenness of their time centering assumptions and retaining their simple algorithmic structure burton s conservative scheme 1991 is found as a special case of time centering which cancels the term here designated as incompatible displacements residue in contrast von neumann richtmyer s original centering can be preserved provided this residue is properly corrected these two schemes are the only special cases able to capture isentropic flow with a third order entropy error instead of second order in general the momentum equation is presently obtained by application of a variational principle to an action integral discretized in both space and time the internal energy equation follows from the discrete conservation of total energy entropy production by artificial dissipation is obtained to second order by a prediction correction step on the momentum equation the overall structure of the equations explicit for momentum locally implicit for internal energy remains identical to that of usual sts leap frog schemes though complementary terms are required to correct the effects of time step changes and artificial viscosity updates in deriving these schemes an apparently novel approach of flux in time was introduced to correct numerical residues and ensure energy conservation this method can be applied to essentially any numerical scheme whenever required or desired provided space and time numerical consistency is preserved numerical test cases are presented confirming the conservative character of the new csts schemes down to computer round off errors and showing various improvements compared to the standard von neumann richtmyer and wilkins sts schemes mostly on shock levels shock velocities singularity induced distortions and cfl stability limits

blind source separation based on time frequency signal representations blind source separation consists of recovering a set of signals of which only instantaneous linear mixtures are observed thus far this problem has been solved using statistical information available on the source signals this paper introduces a new blind source separation approach exploiting the difference in the time frequency t f signatures of the sources to be separated the approach is based on the diagonalization of a combined set of spatial t f distributions in contrast to existing techniques the proposed approach allows the separation of gaussian sources with identical spectral shape but with different t f localization properties the effects of spreading the noise power while localizing the source energy in the t f domain amounts to increasing the robustness of the proposed approach with respect to noise and hence improved performance asymptotic performance analysis and numerical simulations are provided

elimination of artificial grid distortion and hourglass type motions by means of lagrangian subzonal masses and pressures the bane of lagrangian hydrodynamics calculations is the premature breakdown of grid topology that results in severe degradation of accuracy and run termination often long before the assumption of a lagrangian zonal mass has ceased to be valid at short spatial grid scales this is usually referred to by the terms hourglass mode or keystone motion associated in particular with underconstrained grids such as quadrilaterals and hexahedrons in two and three dimensions respectively at longer spatial lengths relative to the grid spacing there is what is referred to ubiquitously as spurious vorticity or the long thin zone problem in both cases the result is anomalous grid distortion and tangling that has nothing to do with the actual solution as would be the case for turbulent flow in this work we show how such motions can be eliminated by the proper use of subzonal lagrangian masses and associated densities and pressures these subzonal pressures give rise to forces that resist these spurious motions the pressure is no longer a constant in a zone it now accurately reflects the density gradients that can occur within a zone due to its differential distortion subzonal lagrangian masses can be choosen in more than one manner to obtain subzonal density and pressure variation however these masses arise in a natural way from the intersection of the lagrangian contours through which no mass flows that are associated with both the lagrangian zonal and nodal masses in a staggered spatial grid hydrodynamics formulation this is an extension of the usual lagrangian assumption that is often applied to only the zonal mass we show that with a proper discretization of the subzonal forces resulting from subzonal pressures hourglass motion and spurious vorticity can be eliminated for a very large range of problems

robustness analysis of spatial time frequency distributions based on the influence function standard spatial time frequency distribution stfd estimators derived based on the gaussian noise assumption are known to have poor performance in the case of impulsive noise recently different stfd estimators have been proposed which based on simulations are claimed to be robust in this paper we provide an influence function robustness analysis of stfd estimators we derive the influence functions for the asymptotic and for the finite sample case and study robustness of the standard as well as for some recently proposed robust stfd estimators the empirical influence function gives practitioners a simple way to pre select stfd estimators for their scenario our analysis confirms that unlike for the standard estimator the proposed robust estimators yield a bounded influence function and are robust over a broad class of distributions future research on stfd estimation will allow for the design of robust and efficient estimators based on the influence function

truncation criteria and algorithm for the reduction to normal form of catastrophe unfoldings ii singularities with non zero rank the truncation theorem for the reduction of unfoldings to normal form to specified degree in the control variables is generalized to unfoldings of singularities having non zero rank by using the splitting lemma generalized to unfoldings it is shown that inhomogeneous linear state space transformations suffice for the splitting to determine the normal forms for both singularities and unfoldings although not the mappings a splitting algorithm is given that may be implemented by computer algebra and together with previous work allows an arbitrary elementary catastrophe to be reduced to normal form

a high order cell centered lagrangian scheme for compressible fluid flows in two dimensional cylindrical geometry the goal of this paper is to present high order cell centered schemes for solving the equations of lagrangian gas dynamics written in cylindrical geometry a node based discretization of the numerical fluxes is obtained through the computation of the time rate of change of the cell volume it allows to derive finite volume numerical schemes that are compatible with the geometric conservation law gcl two discretizations of the momentum equations are proposed depending on the form of the discrete gradient operator the first one corresponds to the control volume scheme while the second one corresponds to the so called area weighted scheme both formulations share the same discretization for the total energy equation in both schemes fluxes are computed using the same nodal solver which can be viewed as a two dimensional extension of an approximate riemann solver the control volume scheme is conservative for momentum total energy and satisfies a local entropy inequality in its first order semi discrete form however it does not preserve spherical symmetry on the other hand the area weighted scheme is conservative for total energy and preserves spherical symmetry for one dimensional spherical flow on equi angular polar grid the two dimensional high order extensions of these two schemes are constructed employing the generalized riemann problem grp in the acoustic approximation many numerical tests are presented in order to assess these new schemes the results obtained for various representative configurations of one and two dimensional compressible fluid flows show the robustness and the accuracy of our new schemes

a subcell remapping method on staggered polygonal grids for arbitrary lagrangian eulerian methods we describe a new remapping algorithm for use in arbitrary lagrangian eulerian ale simulations the new features of this remapper are designed to complement a staggered mesh lagrangian phase in which the cells may be general polygons in two dimensions and which uses subcell discretizations to control unphysical mesh distortion and hourglassing our new remapping algorithm consists of three stages a gathering stage in which we interpolate momentum internal energy and kinetic energy to the subcells in a conservative way a subcell remapping stage in which we conservatively remap mass momentum internal and kinetic energy from the subcells of the lagrangian mesh to the subcells of the new rezoned mesh a scattering stage in which we conservatively recover the primary variables subcell density nodal velocity and cell centered specific internal energy on the new rezoned mesh we prove that our new remapping algorithm is conservative reversible and satisfies the debar consistency condition we also demonstrate computationally that our new remapping method is robust and accurate for a series of test problems in one and two dimensions

algebraic limitations on two dimensional hydrodynamics simulations algebraic limitations imposed by the use of connected straightline segments to define meshes for hydrodynamics simulations in two dimensional cylindrical geometries are shown it is shown that in the simplest smooth isentropic flow of the spherical expansion of a gas with point symmetry commonly and currently used finite difference finite volume or finite element staggered grid hydrodynamics equations cannot simultaneously preserve energy entropy and sphericity on an equal angler mesh it is further shown why finite difference codes tend to preserve sphericity and entropy while finite element codes tend to preserve sphericity and energy exact difference representations of interface cell face pressures and work terms and of the elements of the strain rate tensor in a cell are shown

the force work differencing of exceptional points in the discrete compatible formulation of lagrangian hydrodynamics this study presents the force and mass discretization of exceptional points in the compatible formulation of lagrangian hydrodynamics it concludes a series of papers that develop various aspects of the theoretical exposition and the operational implementation of this numerical algorithm exceptional points are grid points at the termination of lines internal to the computational domain and where boundary conditions are therefore not applied these points occur naturally in most applications in order to ameliorate spatial grid anisotropy and the consequent timestep reduction that will otherwise arise for grids with highly tapered regions or a center of convergence they have their velocity enslaved to that of neighboring points in order to prevent large excursions of the numerical solution about them how this problem is treated is given herein for the aforementioned numerical algorithm such that its salient conservation properties are retained in doing so the subtle aspects of this algorithm that are due to the interleaving of spatial contours that occur with the use of a spatially staggered grid mesh are illuminated these contours are utilized to define both forces and the work done by them and are the central construct of this type of finite volume differencing additionally difficulties that occur due to uncertainties in the specification of the artificial viscosity are explored and point to the need for further research in this area

spatial averaging of time frequency distributions for signal recovery in uniform linear arrays this paper presents a new approach based on spatial time frequency averaging for separating signals received by a uniform linear antenna array in this approach spatial averaging of the time frequency distributions tfds of the sensor data is performed at multiple time frequency points this averaging restores the diagonal structure of the source tfd matrix necessary for source separation with spatial averaging cross terms move from their off diagonal positions in the source tfd matrix to become part of the matrix diagonal entries it is shown that the proposed approach yields improved performance over the case when no spatial averaging is performed further we demonstrate that in the context of source separation the spatially averaged wigner ville distribution outperforms the combined spatial time frequency averaged distributions such as the one obtained by using the choi williams 1989 distribution simulation examples involving the separation of two sources with close am and fm modulations are presented

a two dimensional unstructured cell centered multi material ale scheme using vof interface reconstruction we present a new cell centered multi material arbitrary lagrangian eulerian ale scheme to solve the compressible gas dynamics equations on two dimensional unstructured grid our ale method is of the explicit time marching lagrange plus remap type namely it involves the following three phases a lagrangian phase wherein the flow is advanced using a cell centered scheme a rezone phase in which the nodes of the computational grid are moved to more optimal positions a cell centered remap phase which consists of interpolating conservatively the lagrangian solution onto the rezoned grid the multi material modeling utilizes either concentration equations for miscible fluids or the volume of fluid vof capability with interface reconstruction for immiscible fluids the main original feature of this ale scheme lies in the introduction of a new mesh relaxation procedure which keeps the rezoned grid as close as possible to the lagrangian one in this formalism the rezoned grid is defined as a convex combination between the lagrangian grid and the grid resulting from condition number smoothing this convex combination is constructed through the use of a scalar parameter which is a scalar function of the invariants of the cauchy green tensor over the lagrangian phase regarding the cell centered remap phase we employ two classical methods based on a partition of the rezoned cell in terms of its overlap with the lagrangian cells the first one is a simplified swept face based method whereas the second one is a cell intersection based method our multi material ale methodology is assessed through several demanding two dimensional tests the corresponding numerical results provide a clear evidence of the robustness and the accuracy of this new scheme

a compatible energy and symmetry preserving lagrangian hydrodynamics algorithm in three dimensional cartesian geometry this work presents a numerical algorithm for the solution of fluid dynamics problems with moderate to high speed flow in three dimensions cartesian geometry is chosen owing to the fact that in this coordinate system no curvature terms are present that break the conservation law structure of the fluid equations written in lagrangian form these equations are discretized utilizing compatible control volume differencing with a staggered grid placement of the spatial variables the concept of compatibility means that the forces used in the momentum equation to advance velocity are also incorporated into the internal energy equation so that these equations together define the total energy as a quantity that is exactly conserved in time in discrete form multiple pressures are utilized in each zone they produce forces that resist spurious vorticity generation this difficulty can severely limit the utility of the lagrangian formulation in two dimensions and make this representation otherwise virtually useless in three dimensions an edge centered artificial viscosity whose magnitude is regulated by local velocity gradients is used to capture shocks the particular difficulty of exactly preserving one dimensional spherical symmetry in three dimensional geometry is solved this problem has both practical and pedagogical significance the algorithm is suitable for both structured and unstructured grids limitations that symmetry preservation imposes on the latter type of grids are delineated

reducing the entropy production in a collocated lagrange remap scheme the eulerian scheme described in this article aims to perform efficient and accurate compressible multimaterial fluid flows simulations we use a second order collocated lagrange remap scheme based on the eucclhyd lagrangian scheme maire et al 2007 26 which is conservative and uses acoustic riemann solvers the entropy production is studied and a correction is proposed to improve accuracy in isentropic flows by adding correction fluxes the scheme is thus kept conservative in mass momentum and total energy a vof plic interface reconstruction is added to the scheme results are presented that assess the dissipation reduction

a cell centered lagrangian scheme for two dimensional compressible flow problems we present a new lagrangian cell centered scheme for two dimensional compressible flows the primary variables in this new scheme are cell centered i e density momentum and total energy are defined by their mean values in the cells the vertex velocities and the numerical fluxes through the cell interfaces are not computed independently contrary to standard approaches but are evaluated in a consistent manner due to an original solver located at the nodes the main new feature of the algorithm is the introduction of four pressures on each edge two for each node on each side of the edge this extra degree of freedom allows us to construct a nodal solver which fulfills two properties first the conservation of momentum and total energy is ensured second a semidiscrete entropy inequality is provided in the case of a one dimensional flow the solver reduces to the classical godunov acoustic solver it can be considered as its two dimensional generalization many numerical tests are presented they are representative test cases for compressible flows and demonstrate the robustness and the accuracy of this new solver

high order multi material ale hydrodynamics we present a new approach for multi material arbitrary lagrangian eulerian ale hydrodynamics simulations based on high order finite elements posed on high order curvilinear meshes the method builds on and extends our previous work in the lagrangian v a dobrev t v kolev and r n rieben siam j sci comput 34 2012 pp b606 b641 and remap r w anderson et al internat j numer methods fluids 77 2015 pp 249 273 phases of ale and depends critically on a functional perspective that enables subzonal physics and material modeling v a dobrev et al internat j numer methods fluids 82 2016 pp 689 706 curvilinear mesh relaxation is based on node movement which is determined through the solution of an elliptic equation the remap phase is posed in terms of advecting state variables between two meshes over a fictitious time interval the resulting advection equation is solved by a discontinuous galerkin dg formulation combined with a customized flux corrected transpor

influence function and asymptotic efficiency of scatter matrix based array processors case mvdr beamformer in this paper we consider array processors that are scale invariant functions of the array covariance matrix the emphasis is on capon s mvdr beamformer we call such an array processor as scatter matrix based smb array processor since the covariance matrix is required only up to a constant scalar and thus a scatter matrix proportional to covariance under finite covariance assumption provides sufficient information in order to establish interesting statistical robustness and large sample properties we derive a general expression for the influence function and the asymptotic covariance structure of smb mvdr beamformer weights our results apply under the class of complex elliptically symmetric distributions which includes the commonly used complex normal distribution as a special case we illustrate the theory by deriving the if and asymptotic relative efficiencies of the conventional smb mvdr beamformer that employs the sample covariance matrix and beamformers that employ robust m estimators of scatter theoretical findings are confirmed by simulations our findings favor beamformers based upon m estimators of scatter since they combine a high efficiency with appealing robustness properties

compatible total energy conserving and symmetry preserving arbitrary lagrangian eulerian hydrodynamics in 2d rz cylindrical coordinates we present a new discretization for 2d arbitrary lagrangian eulerian hydrodynamics in rz geometry cylindrical coordinates that is compatible total energy conserving and symmetry preserving in the first part of the paper we describe the discretization of the basic lagrangian hydrodynamics equations in axisymmetric 2d rz geometry on general polygonal meshes it exactly preserves planar cylindrical and spherical symmetry of the flow on meshes aligned with the flow in particular spherical symmetry is preserved on polar equiangular meshes the discretization conserves total energy exactly up to machine round off on any mesh it has a consistent definition of kinetic energy in the zone that is exact for a velocity field with constant magnitude the method for discretization of the lagrangian equations is based on ideas presented in 2 3 7 where the authors use a special procedure to distribute zonal mass to corners of the zone subzonal masses the momentum equation is discretized in its cartesian form with a special definition of planar masses area weighted the principal contributions of this part of the paper are as follows a definition of planar subzonal mass for nodes on the z axis r 0 that does not require a special procedure for movement of these nodes proof of conservation of the total energy formulated for general polygonal meshes we present numerical examples that demonstrate the robustness of the new method for lagrangian equations on a variety of grids and test problems including polygonal meshes in particular we demonstrate the importance of conservation of total energy for correctly modeling shock waves in the second part of the paper we describe the remapping stage of the arbitrary lagrangian eulerian algorithm the general idea is based on the following papers 25 28 where it was described for cartesian coordinates we describe a distribution based algorithm for the definition of remapped subzonal densities and a local constrained optimization based approach for each zone to find the subzonal mass fluxes in this paper we give a systematic and complete description of the algorithm for the axisymmetric case and provide justification for our approach 1 the ale algorithm conserves total energy on arbitrary meshes and preserves symmetry when remapping from one equiangular polar mesh to another the principal contributions of this part of the paper are the extension of this algorithm to general polygonal meshes and 2d rz geometry with requirement of symmetry preservation on special meshes we present numerical examples that demonstrate the robustness of the new ale method on a variety of grids and test problems including polygonal meshes and some realistic experiments we confirm the importance of conservation of total energy for correctly modeling shock waves

subspace analysis of spatial time frequency distribution matrices spatial time frequency distributions stfds have been previously introduced as the natural means to deal with source signals that are localizable in the time frequency domain previous work in the area has not provided the eigenanalysis of stfd matrices which is key to understanding their role in solving direction finding and blind source separation problems in multisensor array receivers the aim of this paper is to examine the eigenstructure of the stfd matrices we develop the analysis and statistical properties of the subspace estimates based on stfds for frequency modulated fm sources it is shown that improved estimates are achieved by constructing the subspaces from the time frequency signatures of the signal arrivals rather than from the data covariance matrices which are commonly used in conventional subspace estimation methods this improvement is evident in a low signal to noise ratio snr environment and in the cases of closely spaced sources the paper considers the music technique to demonstrate the advantages of stfds and uses it as grounds for comparison between time frequency and conventional subspace estimates

algebraic multigrid for linear systems obtained by explicit element reduction we consider sparse linear systems where a set of interior degrees of freedom have been eliminated in order to reduce the problem size this elimination is assumed to be local so the interior principal submatrix is block diagonal and the resulting schur complement is still sparse for it to be beneficial the elimination process should lead to reduced memory requirements but equally importantly it should also result in an algebraic problem that can be solved efficiently in this paper we propose a general element reduction approach and show how the elimination process can exploit a particular subzonal discretization to maintain the sparsity of the schur complement we also investigate algebraic multigrid amg solution algorithms applied to the reduced problem and we discuss the influence of the local elimination on solver related properties of the matrix such as near nullspace preservation and the availability of stable subspace decompositions we focus on boomeramg a parallel variant of classical ruge stuben amg applied to scalar diffusion problems v henson and u yang appl numer math 41 2002 pp 155 177 and the auxiliary space maxwell solver ams for electromagnetic diffusion applications t kolev and p vassilevski j comput math 27 2009 pp 604 623 in the electromagnetic case we establish algebraically a reduced version of the hiptmair xu decomposition from r hiptmair and j xu siam j numer anal 45 2007 pp 2483 2509 and consider a modification of the reduction process that targets the singular problems arising in simulations with pure void zero conductivity regions for scalar diffusion problems our particular stencil analysis shows that the reduction has a positive effect on meshes with stretched elements we present a number of two dimensional three dimensional and axisymmetric numerical experiments which demonstrate that the combination of an appropriately chosen local elimination with the use of the boomeramg and ams solvers can lead to significant improvements in the overall solution time

robust l estimation based forms of signal transforms and time frequency representations the l estimation based signal transforms and time frequency tf representations are introduced by considering the corresponding minimization problems in the huber 1981 1998 estimation theory the standard signal transforms follow as the maximum likelihood solutions for the gaussian additive noise environment for signals corrupted by an impulse noise the median based transforms produce robust estimates of the non noisy signal transforms when the input noise is a mixture of gaussian and impulse noise the l estimation based signal transforms can outperform other estimates in quadratic and higher order tf analysis the resulting noise is inherently a mixture of the gaussian input noise and an impulse noise component in this case the l estimation based signal representations can produce the best results these transforms and tf representations give the standard and the median based forms as special cases a procedure for parameter selection in the l estimation is proposed the theory is illustrated and checked numerically

constrained optimization framework for interface aware sub scale dynamics closure model for multimaterial cells in lagrangian and arbitrary lagrangian eulerian hydrodynamics abstract a systematic description of the new interface aware sub scale dynamics ia ssd closure model for the lagrangian stage of multimaterial arbitrary lagrangian eulerian methods is presented the ia ssd closure model consists of two stages during the first bulk stage the well known equal compressibility model is used during the second stage sub scale interactions of the materials inside the multimaterial cell are taken into account at this stage information about the topology of the materials inside the multimaterial cell is utilized allowing the orientations of internal interfaces to be included in the model each material interacts in a pair wise fashion with the materials with which it has a common boundary the interactions are based on the solution of the acoustic riemann problem between each pair of materials and is limited using physically justified constraints positivity of volume positivity of internal energy and controlled rate of pressure relaxation to determine the values of the limiter coefficients a constrained optimization framework is employed using a quadratic objective function with linear constraints the algorithm guarantees the positivity of the material volume and internal energy as well as the smooth relaxation of the pressure this allows a significant increase in the robustness of the overall algorithm the results of comprehensive testing of the new model have been presented for one and two dimensional multimaterial lagrangian hydrodynamics along with representative results for 2d multimaterial arbitrary lagrangian eulerian ale calculations the numerical tests have shown that in most cases the new ia ssd closure model produces better results compared to the well known tipton s closure model

two new three dimensional contact algorithms for staggered lagrangian hydrodynamics abstract this paper presents two new three dimensional contact algorithms for staggered lagrangian hydrodynamics named discrete accurate matching method and discrete lagrangian multiplier method these new contact algorithms utilize the unified contact algorithm for contact searching contact segments from all potential contact surfaces are treated as a single set the basic idea of these new methods is to partition all contact segments into triangular facets firstly then for each pair of two triangular facets which correspond to a hitting node and a target node respectively these two triangular facets are projected to one plane and their intersection area is calculated the nodal masses and nodal forces of the hitting node and the target node are distributed to the intersection portions of these two triangular facets respectively according to the proportion of the intersection area to corresponding nodal area in the discrete accurate matching method the masses and forces of the intersection portions of these two triangular facets are added to corresponding contact nodes of each other and then the accelerations and velocities of the contact nodes are updated while in the discrete lagrangian multiplier method the intersection portions of these two triangular facets are considered as a 1d contact pair in the normal direction for which the contact force is explicitly calculated by the lagrangian multiplier method for a 1d contact pair of one hitting point and one target point then the contact force being added to corresponding contact nodes these new contact algorithms are assessed through several numerical tests performed on three dimensional structured and unstructured meshes the results of these tests show the accuracy and robustness of these new methods

non gaussian noise models in signal processing for telecommunications new methods an results for class a and class b noise models the subject here is generalized i e non gaussian noise models and specifically their first order probability density functions pdfs attention is focused primarily on the author s canonical statistical physical class a and class b models in particular class a noise describes the type of electromagnetic interference emi often encountered in telecommunication applications where this ambient noise is largely due to other intelligent telecommunication operations on the other hand ambient class b noise usually represents man made or natural nonintelligent i e nonmessage bearing noise and is highly impulsive class a noise is not an spl alpha stable process nor is it reducible to such except in the limiting gaussian cases of high density noise by the central limit theorem class b noise is also asymptotically normal before model approximation under rather broad conditions principally governed by the source propagation and distribution scenarios the pdf of class b noise alone no gaussian component can usually be approximated by 1 a symmetric gaussian spl alpha stable s spl alpha s model in the case of narrowband reception or when the pdf spl omega sub 1 spl alpha of the amplitude is symmetric and 2 a nonsymmetric spl alpha stable ns spl alpha s model no gaussian component can be constructed in broadband regimes new results here include i counting functional methods for constructing the general qth order characteristic functions cfs of class a and class b noise from which all moments and in principle the pdfs follow ii the first order cfs pdfs and cumulative probabilities apds of nonsymmetric broadband class b noise extended to include additive gauss noise agn iii proof of the existence of all moments in the basic class a and class b models iv the key physical role of agn and the fact that agn removes spl alpha stability v the explicit roles of the propagation and distribution scenarios and vi extension to noise fields although telecommunication applications are emphasized class a and class b noise models apply selectively but equally well to other physical regimes e g underwater acoustics and em radar optics etc supportive empirical data are included

high order staggered schemes for compressible hydrodynamics weak consistency and numerical validation abstract staggered grids schemes formulated in internal energy are commonly used for cfd applications in industrial context here we prove the consistency of a class of high order lagrange remap staggered schemes for solving the euler equations in 1d and 2d on cartesian grids the main result of the paper is that using an a posteriori internal energy corrector the lagrangian schemes are proved to be conservative in mass momentum and total energy and to be weakly consistent with the 1d lagrangian formulation of the euler equations extension in 2d is done using directional splitting methods and face staggering numerical examples in both 1d and 2d illustrate the accuracy the convergence and the robustness of the schemes

a cell centered lagrangian scheme with the preservation of symmetry and conservation properties for compressible fluid flows in two dimensional cylindrical geometry we develop a new cell centered control volume lagrangian scheme for solving euler equations of compressible gas dynamics in cylindrical coordinates the scheme is designed to be able to preserve one dimensional spherical symmetry in a two dimensional cylindrical geometry when computed on an equal angle zoned initial grid unlike many previous area weighted schemes that possess the spherical symmetry property our scheme is discretized on the true volume and it can preserve the conservation property for all the conserved variables including density momentum and total energy several two dimensional numerical examples in cylindrical coordinates are presented to demonstrate the performance of the scheme in terms of symmetry accuracy and non oscillatory properties

reduced dissipation remapping of velocity in staggered arbitrary lagrangian eulerian methods remapping is an essential part of most arbitrary lagrangian eulerian ale methods in this paper we focus on the part of the remapping algorithm that performs the interpolation of the fluid velocity field from the lagrangian to the rezoned computational mesh in the context of a staggered discretization standard remapping algorithms generate a discrepancy between the remapped kinetic energy and the kinetic energy that is obtained from the remapped nodal velocities which conserves momentum in most ale codes this discrepancy is redistributed to the internal energy of adjacent computational cells which allows for the conservation of total energy this approach can introduce oscillations in the internal energy field which may not be acceptable we analyze the approach introduced in bailey 1984 11 which is not supposed to introduce dissipation on a simple example we demonstrate a situation in which this approach fails a modification of this approach is described which eliminates when it is possible or reduces the energy discrepancy

an asymptotic preserving multidimensional ale method for a system of two compressible flows coupled with friction abstract we present a multidimensional asymptotic preserving scheme for the approximation of a mixture of compressible flows fluids are modelled by two euler systems of equations coupled with a friction term the asymptotic preserving property is mandatory for this kind of model to derive a scheme that behaves well in all regimes i e whatever the friction parameter value is the method we propose is defined in ale coordinates using a lagrange plus remap approach this imposes a multidimensional definition and analysis of the scheme

some cell centered lagrangian laxwendroff hll hybrid schemes lagrangian hydrodynamics is treated by the laxwendroff method with the dissipative fluxes in the hll form including both artificial viscosity and artificial energy flux the symmetry of results for the noh problem on a cartesian mesh is very good on material interfaces we employ the eucclhyd nodal solver at the interface nodes with 1d acoustic approximate riemann solver on the interface edges the proposed method works reasonably well on several hydrodynamic tests including noh sedov saltzman sod woodwardcollela and triple point

mass momentum and energy conserving mamec discretizations on general grids for the compressible euler and shallow water equations the paper explains a method by which discretizations of the continuity and momentum equations can be designed such that they can be combined with an equation of state into a discrete energy equation the resulting mamec discretizations conserve mass momentum as well as energy although no explicit conservation law for the total energy is present essential ingredients are i discrete convection that leaves the discrete energy invariant and ii discrete consistency between the thermodynamic terms of particular relevance is the way in which finite volume fluxes are related to nodal values the method is an extension of existing methods based on skew symmetry of discrete operators because it allows arbitrary equations of state and a larger class of grids than earlier methods the method is first illustrated with a one dimensional example on a highly stretched staggered grid in which the mamec method calculates qualitatively correct results and a non skew symmetric finite volume method becomes unstable a further example is a two dimensional shallow water calculation on a rectilinear grid as well as on an unstructured grid the conservation of mass momentum and energy is checked and losses are found negligible up to machine accuracy

a new exceptional points method with application to cell centered lagrangian schemes and curved meshes the aim of this paper is the numerical simulation of compressible hydrodynamic strong implosions which take place for instance in inertial confinement fusion it focuses in particular on two crucial issues for such calculations very low cfl number at the implosion center and approximation error on the initial geometry thus we propose an exceptional points method which is translation invariant and suitable to curved meshes this method is designed for cell centered lagrangian schemes glace 8 13 14 eucclhyd 25 29 several numerical examples on significant test cases are presented to show the relevance of our approach

revisiting wall heating the results of computing a shock reflection are found to strongly depend on the chosen coordinate system lagrangian or eulerian this is seen by comparing the amount of wall heating associated with the solutions to noh s shock reflection problem computed in each reference frame here an explanation is offered that places a greater burden on the role of phase error or effective wave speed in producing this effect the reason for the greater difficulties in the lagrangian frame are the non uniformity of the mass coordinates in a converging geometry this produces a non steady state discrete shock profile

a subzone reconstruction algorithm for efficient staggered compatible remapping staggered grid lagrangian hydrodynamics algorithms frequently make use of subzonal discretization of state variables for the purposes of improved numerical accuracy generality to unstructured meshes and exact conservation of mass momentum and energy for arbitrary lagrangian eulerian ale methods using a geometric overlay it is difficult to remap subzonal variables in an accurate and efficient manner due to the number of subzone subzone intersections that must be computed this becomes prohibitive in the case of 3d unstructured polyhedral meshes a new procedure is outlined in this paper to avoid direct subzonal remapping the new algorithm reconstructs the spatial profile of a subzonal variable using remapped zonal and nodal representations of the data the reconstruction procedure is cast as an under constrained optimization problem enforcing conservation at each zone and node on the remapped mesh provides the set of equality constraints the objective function corresponds to a quadratic variation per subzone between the values to be reconstructed and a set of target reference values numerical results for various pure remapping and hydrodynamics tests are provided ideas for extending the algorithm to staggered grid radiation hydrodynamics are discussed as well as ideas for generalizing the algorithm to include inequality constraints

operator splitting and time accuracy in lagrange plus remap solution methods operator splitting and time accuracy in lagrange plus remap solution methods for the hydrodynamics equations are investigated the time accuracy of the common solution approach is shown both analytically and numerically to be limited to first order due to operator splitting errors low order time integration of the remap terms and other postulated first order errors even if the lagrange step is second order accurate in time additional numerical studies are used to demonstrate how these errors can be eliminated with an unsplit treatment that solves the remap terms directly the discontinuous remap method in which a new mesh is generated during the remap step also is shown to be first order accurate in time

a lagrangian staggered grid godunov like approach for hydrodynamics much research in lagrangian staggered grid hydrodynamics sgh has focused on explicit viscosity models for adding dissipation to a calculation that has shocks the explicit viscosity is commonly called artificial viscosity recently researchers have developed hydrodynamic algorithms that incorporate approximate riemann solutions on the dual grid 28 29 35 30 2 3 this approach adds dissipation to the calculation via solving a riemann like problem in this work we follow the works of 28 29 35 30 and solve a multidirectional riemann like problem at the cell center the riemann like solution at the cell center is used in the momentum and energy equations the multidirectional riemann like problem used in this work differs from previous work in that it is an extension of the cell centered hydrodynamics cch nodal solution approach in 7 incorporating the multidirectional riemann like problem from 7 into sgh has merits such as the ability to resist mesh instabilities like hourglass null modes and chevron null modes the approach is valid for complex multidimensional flows with strong shocks numerical details and test problems are presented

a discontinuous galerkin discretization for solving the two dimensional gas dynamics equations written under total lagrangian formulation on general unstructured grids based on the total lagrangian kinematical description a discontinuous galerkin dg discretization of the gas dynamics equations is developed for two dimensional fluid flows on general unstructured grids contrary to the updated lagrangian formulation which refers to the current moving configuration of the flow the total lagrangian formulation refers to the fixed reference configuration which is usually the initial one in this framework the lagrangian and eulerian descriptions of the kinematical and the physical variables are related by means of the piola transformation here we describe a cell centered high order dg discretization of the physical conservation laws the geometrical conservation law which governs the time evolution of the deformation gradient is solved by means of a finite element discretization this approach allows to satisfy exactly the piola compatibility condition regarding the dg approach it relies on the use of a polynomial space approximation which is spanned by a taylor basis the main advantage in using this type of basis relies on its adaptability regardless the shape of the cell the numerical fluxes at the cell interfaces are computed employing a node based solver which can be viewed as an approximate riemann solver we present numerical results to illustrate the robustness and the accuracy up to third order of our dg method first we show its ability to accurately capture geometrical features of a flow region employing curvilinear grids second we demonstrate the dramatic improvement in symmetry preservation for radial flows

an approach for treating contact surfaces in lagrangian cell centered hydrodynamics a new method is presented for modeling contact surfaces in lagrangian cell centered hydrodynamics cch the contact method solves a multi directional riemann like problem at each penetrating or touching node along the contact surface the velocity of a penetrating or touching node and the corresponding forces are explicitly calculated using the riemann like nodal solver the contact method works with material strength and allows surfaces to impact slide and separate results are presented for several test problems involving both gases and materials with strength the new contact surface approach extends the modeling capabilities of cch

on stability of staggered schemes this paper investigates the theoretical stability bound of a lagrangian staggered scheme used to solve hydrodynamics equations we present the two dimensional 2d wave equation as a possible model for this study and by using the numerical radius of the amplification matrix we prove that the family of schemes defined with two time centering parameters is limited by a nonclassical stability bound limit defined with an analytical curve we further show that 2d numerical experiments agree with this theoretical result

a multi scale residual based anti hourglass control for compatible staggered lagrangian hydrodynamics abstract hourglassing is a well known pathological numerical artifact affecting the robustness and accuracy of lagrangian methods there exist a large number of hourglass control suppression strategies in the community of the staggered compatible lagrangian methods the approach of sub zonal pressure forces is among the most widely used however this approach is known to add numerical strength to the solution which can cause potential problems in certain types of simulations for instance in simulations of various instabilities to avoid this complication we have adapted the multi scale residual based stabilization typically used in the finite element approach for staggered compatible framework in this paper we describe two discretizations of the new approach and demonstrate their properties and compare with the method of sub zonal pressure forces on selected numerical problems

formulations of artificial viscosity for multi dimensional shock wave computations in this paper we present a new formulation of the artificial viscosity concept physical arguments for the origins of this term are given and a set of criteria that any proper functional form of the artificial viscosity should satisfy is enumerated the first important property is that by definition a viscosity must always be dissipative transferring kinetic energy into internal energy and must never act as a false pressure the artificial viscous force should be galilean invariant and vary continuously as a function of the criterion used to determine compression and expansion and remain zero for the latter case these requirements significantly constrain the functional form that the artificial viscous force can have in addition an artificial viscosity should be able to distinguish between shock wave and adiabatic compression and not result in spurious entropy production when only the latter is present it must therefore turn off completely for self similiar motion where only a uniform stretching and or a rigid rotation occurs an additional important but more subtle condition where the artificial viscosity should produce no effect is along the direction tangential to a convergent shock front since the velocity is only discontinuous in the normal direction our principal result is the development of a new formulation of an edge centered artificial viscosity that is to be used in conjunction with a staggered spatial placement of variables that meets all of these standards and without the need for problem dependent numerical coefficients that have in the past made the artificial viscosity method appear somewhat arbitrary our formulation and numerical results are given with respect to two spatial dimensions but all of our arguments carry over directly to three dimensions a central feature of our development is the implementation of simple advection limiters in a straightforward manner in more than one dimension to turn off the artificial viscosity for the above mentioned conditions and to substantially reduce its effect when strong velocity gradients are absent

numerical preservation of symmetry properties of continuum problems we investigate the problem of perfectly preserving a symmetry associated naturally with one coordinate system when calculated in a different coordinate system this allows a much wider range of problems that may be viewed as perturbations of the given symmetry to be investigated we study the problem of preserving cylindrical symmetry in two dimensional cartesian geometry and spherical symmetry in two dimensional cylindrical geometry we show that this can be achieved by a simple modification of the gradient operator used to compute the force in a staggered grid lagrangian hydrodynamics algorithm in the absence of the supposed symmetry we show that the new operator produces almost no change in the results because it is always close to the original gradient operator our technique thus results in a subtle manipulation of the spatial truncation error in favor of the assumed symmetry but only to the extent that it is naturally present in the physical situation this not only extends the range of previous algorithms and the use of new ones for these studies but for spherical or cylindrical calculations it reduces the sensitivity of the results to grid setup with equal angular zoning that has heretofore been necessary with these problems

stabilization of cell centered compressible lagrangian methods using subzonal entropy this work deals with the stabilization of early stages of lagrangian calculations of compressible gas dynamics in the context of cell centered discretization we describe a totally conservative algorithm based on an entropy analysis of the distortion of a lagrangian mesh it prevents the tangling of the mesh while remaining consistent and conservative in mass momentum and total energy the method described can be applied to any cell centered lagrangian scheme in this article we detail the extension to the cell centered glace scheme published in carre et al 2009 g carre s del pino b despres e labourasse a cell centered lagrangian hydrodynamics scheme on general unstructured meshes in arbitrary dimension j comput phys 228 2009 5160 5183 numerical tests are proposed to assess the accuracy and robustness

vorticity errors in multidimensional lagrangian codes abstract we investigate the apparent paradox as exemplified by the well known saltzman test problem of multidimensional lagrangian codes experiencing mesh tangling when computing one dimensional irrotational flows we demonstrate that the cause is the generation of spurious vorticity or vorticity error by a nonuniform mesh based on this we investigate two methods of constructing improved lagrangian vertex velocities by removing or filtering out this spurious vorticity rather than by the more common practice of introducing artificial viscosity the first method reconstructs the velocity from the known flow divergence and from the true vorticity computed by means of a transport equation the second method which is much simpler and more efficient subtracts a divergence free correction from the velocity such that the resulting velocity possesses the correct vorticity we then successfully apply this method to solve a two dimensional shock refraction problem a problem which exhibits nonzero intrinsic vorticity

application of vector calculus to numerical simulation of continuum mechanics problems abstract it is well known that vector tensor notation is a compact and natural language for the mathematical formulation of continuum mechanics problems here we describe the application of vector technique to numerical simulation starting with a mathematical formulation we provide an efficient numerical scheme and furnish an implementation as a computer program as a result in comparison with traditional component form the two last steps are significantly simplified especially for multidimensional problems with various boundary conditions in irregular geo metries where nonorthogonal meshes are applied therefore more attention can be focused on the physical nature of problems apart from the cleaner syntax vector notation conserves the structure of traditional numerical algorithms and solves multidimensional problems with minimum additional programming effort complex practical applications of this technique are described as well

isentropic correction for collocated lagrange remap scheme abstract we study an eulerian scheme of lagrange remap type which simulates compressible multi material fluid flows the lagrangian phase is based on a collocated scheme called eucclhyd explicit unstructured cell centered lagrangian hydrodynamics maire et al 2007 whereas the remap phase uses alternate directions with interface reconstruction of plic type the eucclhyd scheme which is built on the resolution of acoustic riemann problems at nodes is totally conservative second order in time and space and captures shock waves accurately however the intrinsic entropy production is inaccurate for isentropic flows rarefaction expansion waves isentropic compression in this framework we suggest a correction inspired by braeunig 2016 to improve accuracy in flows with isentropic behavior this is achieved by modifying the scheme in order to nullify the entropy production in expansion zones