converging shocks in elastic plastic solids we present an approximate description of the behavior of an elastic plastic material processed by a cylindrically or spherically symmetric converging shock following whitham s shock dynamics theory originally applied with success to various gas dynamics problems this theory is presently derived for solid media in both elastic and plastic regimes the exact solutions of the shock dynamics equations obtained reproduce well the results obtained by high resolution numerical simulations the examined constitutive laws share a compressible neo hookean structure for the internal energy e e s i 1 e h where e s accounts for shear through the first invariant of the cauchy green tensor and e h represents the hydrostatic contribution as a function of the density and entropy in the strong shock limit reached as the shock approaches the axis or origin r 0 we show that compression effects are dominant over shear deformations for an isothermal constitutive law i e e h e h with a power law dependence e h shock dynamics predicts that for a converging shock located at r r t at time t the mach number increases as m log 1 r independently of the space index s where s 2 in cylindrical geometry and 3 in spherical geometry an alternative isothermal constitutive law with p of the arctanh type which enforces a finite density in the strong shock limit leads to m r s 1 for strong shocks a nonisothermal constitutive law whose hydrostatic part eh is that of an ideal gas is also tested recovering the strong shock limit m r s 1 n originally derived by whitham for perfect gases where is inherently related to the maximum compression ratio that the material can reach 1 1 from these strong shock limits we also estimate analytically the density radial velocity pressure and sound speed immediately behind the shock while the hydrostatic part of the energy essentially commands the strong shock behavior the shear modulus and yield stress modify the compression ratio and velocity of the shock far from the axis or origin a characterization of the elastic plastic transition in converging shocks which involves an elastic precursor and a plastic compression region is finally exposed

minimal rotationally invariant bases for hyperelasticity rotationally invariant polynomial bases of the hyperelastic strain energy function are rederived using methods of group theory invariant theory and computational algebra a set of minimal basis functions is given for each of the 11 laue groups with a complete set of rewriting syzygies the ideal generated from this minimal basis agrees with the classic work of smith and rivlin trans amer math soc 88 1958 pp 175 193 however the structure of the invariant algebra described here calls for fewer terms beginning with the fourth degree in strain for most groups

an unsplit higher order godunov method for scalar conservation laws in multiple dimensions abstract in this paper we develop an unsplit higher order godunov method for scalar conservation laws in two dimensions the method represents an extension for the special case being considered of methods developed by colella and by van leer in our method we begin with a piecewise bilinear representation of the solution on each grid cell a new piecewise bilinear representation at the next time level is then obtained from a two step procedure in the first step a conservative predictor corrector scheme derived from the integral form of the differential equation and characteristic considerations is used to obtain average values of the solution over grid cells at the new time level next these new average values are then used to construct a limited piecewise bilinear profile for each cell at the new time level the resulting method is shown to satisfy a maximum principle for constant coefficient linear advection computational results are presented comparing the new method to colella s method for linear advection the method is also applied to two model problems from porous media flow miscible and immiscible displacement the new scheme provides accurate resolution of sharp fronts without any significant distortion

a second order accurate conservative front tracking method in one dimension this paper presents a conservative front tracking method for shocks and contact discontinuities that is second order accurate it is based on a volume of fluid method that treats the moving front with concepts similar to those of an embedded boundary method special care is taken in the centering of the data to ensure the right order of accuracy at the front and a redistribution step guarantees conservation a suite of test problems for tracking both shocks and contact discontinuities is presented that confirms that the method is second order accurate

block structured adaptive mesh and time refinement for hybrid hyperbolic n body systems we present a new numerical algorithm for the solution of coupled collisional and collisionless systems based on the block structured adaptive mesh and time refinement strategy amr we describe the issues associated with the discretization of the system equations and the synchronization of the numerical solution on the hierarchy of grid levels we implement a code based on a higher order conservative and directionally unsplit godunov s method for hydrodynamics a symmetric time centered modified symplectic scheme for collisionless component and a multilevel multigrid relaxation algorithm for the elliptic equation coupling the two components numerical results that illustrate the accuracy of the code and the relative merit of various implemented schemes are also presented

a sharp interface immersed boundary method for compressible viscous flows an immersed boundary method for computing viscous subsonic compressible flows with complex shaped stationary immersed boundaries is presented the method employs a ghost cell technique for imposing the boundary conditions on the immersed boundaries the current approach leads to a sharp representation of the immersed boundaries a property that is especially useful for flow simulations at high reynolds numbers another unique feature of the method is that it can be applied on cartesian as well as generalized body non conformal curvilinear meshes a mixed second order central difference quick scheme is used which allows a high degree of control over the numerical damping a bilinear interpolation scheme used in conjunction with the ghost cell approach results in second order global as well as local spatial accuracy the solver is parallelized for distributed memory platforms using domain decomposition and message passing interface mpi and salient features of the parallel algorithm are presented the accuracy fidelity and efficiency of the solver are examined by simulating flow past circular cylinders and airfoils and comparing against experimental data and other established results finally we present results from a simulation of wing tip flow at a relatively high reynolds number in order to demonstrate the ability of the solver to model complex non canonical three dimensional flows

a conservative three dimensional eulerian method for coupled solid fluid shock capturing a new method is presented for the explicit eulerian finite difference computation of shock capturing problems involving multiple resolved material phases in three dimensions we solve separately for each phase the equations of fluid dynamics or solid mechanics using as interface boundary conditions artificially extended representations of the individual phases for fluids we use a new 3d spatially unsplit implementation of the piecewise parabolic ppm method of colella and woodward for solids we use the 3d spatially unsplit eulerian solid mechanics method of miller and colella vacuum and perfectly incompressible obstacles may also be employed as phases a separate problem is the time evolution of material interfaces which are represented by planar segments constructed with a volume of fluid method the volume fractions are advanced in time using a second order 3d spatially unsplit advection routine with a velocity field determined by solution of interface normal two phase riemann problems from the riemann problem solutions we also determine cross interface momentum and energy fluxes the volume fractions in mixed cells may be arbitrarily small which would ordinarily make the courant friedrichs lewy time step stability limit arbitrarily small as well we overcome this limitation using the mass redistribution formalism to conservatively redistribute generalized mass in the neighborhood of the split cells we present an application of this method to an explosion contained in a metal can a reactive fluid approximating pbx 9404 is encased within an elastic plastic solid approximating copper surrounded by vacuum our implementation is in parallel and with adaptive mesh refinement

short note analytical and geometrical tools for 3d volume of fluid methods in general grids it is well known that volume of fluid vof methods in three dimensions especially those based on unsplit advection schemes involve highly complex geometrical operations the objective of this work is to propose for general grids and three dimensional cartesian geometry simple and efficient geometrical tools for volume truncation operations that typically arise in vof methods and an analytical method for local volume enforcement the results obtained for different tests and grid types show that the proposed analytical method may be as much as three times faster than brent s iterative method advection tests were carried out using hexahedral grids obtained from deformation of a cubic grid to assess the accuracy of the proposed tools in combination with a recently proposed unsplit plic vof method

a cartesian grid embedded boundary method for hyperbolic conservation laws we present a second order godunov algorithm to solve time dependent hyperbolic systems of conservation laws on irregular domains our approach is based on a formally consistent discretization of the conservation laws on a finite volume grid obtained from intersecting the domain with a cartesian grid we address the small cell stability problem associated with such methods by hybridizing our conservative discretization with a stable nonconservative discretization at irregular control volumes and redistributing the difference in the mass increments to nearby cells in a way that preserves stability and local conservation the resulting method is second order accurate in l 1 for smooth problems and is robust in the presence of large amplitude discontinuities intersecting the irregular boundary

multidimensional upwind methods for hyperbolic conservation laws abstract we present a class of second order conservative finite difference algorithms for solving numerically time dependent problems for hyperbolic conservation laws in several space variables these methods are upwind and multidimensional in that the numerical fluxes are obtained by solving the characteristic form of the full multidimensional equations at the zone edge and that all fluxes are evaluated and differenced at the same time in particular operator splitting is not used correct behavior at discontinuities is obtained by the use of solutions to the riemann problem and by limiting some of the second order terms numerical results are presented which show that the methods described here yield the same high resolution as the corresponding operator split methods

efficient solution algorithms for the riemann problem for real gases a procedure for constructing solutions to the riemann problem for gas dynamics with a general convex equation of state is given approximate procedures involving a local parametrization of the equation of state are introduced in order to calculate numerical fluxes in conservative finite difference schemes this leads to difference schemes which are as accurate and almost as fast as the analogous schemes for polytropic gases numerical results in one and two space variables are presented

a 3d adaptive mesh refinement algorithm for multimaterial gas dynamics abstract adaptive mesh refinement amr in conjunction with high order upwind finite difference methods has been used effectively on a variety of problems in this paper we discuss an implementation of an amr finite difference method that solves the equations of gas dynamics with two material species in three dimensions an equation for the evolution of volume fractions augments the gas dynamics system the material interface is preserved and tracked from the volume fractions using a piecewise linear reconstruction technique

interface reconstruction with least squares fit and split advection in three dimensional cartesian geometry in this paper we present and analyze different volume of fluid vof reconstruction and advection algorithms that approximate the interface separating two immiscible fluids in the three dimensional space the paper describes the improvement of the reconstruction when a least square fit algorithm which minimizes a distance functional is applied its performance is tested for several smooth surfaces against other simple reconstruction methods then eulerian lagrangian and mixed split advection schemes are presented and analyzed in particular one advection method is discussed that conserves mass exactly for a divergence free velocity field thus allowing computations to machine precision

second order accurate volume of fluid algorithms for tracking material interfaces we introduce two new volume of fluid interface reconstruction algorithms and compare the accuracy of these algorithms to four other widely used volume of fluid interface reconstruction algorithms we find that when the interface is smooth e g continuous with two continuous derivatives the new methods are second order accurate and the other algorithms are first order accurate we propose a design criteria for a volume of fluid interface reconstruction algorithm to be second order accurate namely that it reproduce lines in two space dimensions or planes in three space dimensions exactly we also introduce a second order unsplit volume of fluid advection algorithm that is based on a second order finite difference method for scalar conservation laws due to bell dawson and shubin we test this advection algorithm by modeling several different interface shapes propagating in two simple incompressible flows and compare the results with the standard second order operator split advection algorithm although both methods are second order accurate when the interface is smooth we find that the unsplit algorithm exhibits noticeably better resolution in regions where the interface has discontinuous derivatives such as at corners

a lattice boltzmann approach for free surface flow simulations on non uniform block structured grids in this paper we present a hybrid volume of fluid based algorithm for the simulation of free surface flow problems for the solution of the flow field the lattice boltzmann method is used the additional advection equation for the volume of fluid vof fill level is discretized with a classical finite volume method for the interface reconstruction a piecewise linear interface reconstruction in 3d has been implemented the free surface tracking algorithm is embedded into the 3d non uniform lattice boltzmann based solver virtualfluids freudiger et al 2009 1 freudiger 2009 2 the advection algorithm is verified and validated with well known advection test cases for the validation of the free surface algorithm we present simulations of a breaking dam benchmark

instantaneous polarization attributes and directional filtering we introduce a systematic definition of instantaneous attributes for an arbitrary multicomponent seismic signal the definition is a natural generalization of known complex trace attributes of a one component signal instantaneous amplitude and all polarization parameters are defined as invariants of instantaneous phase rotation the principal feature of our approach is the unique definition of the instantaneous phase for a signal with any number of components plots of subtle polarization parameters of multicomponent seismic data are easily obtained using conventional seismic plotting routines we illustrate our approach on a synthetic example and apply it to real 3 component wide angle crustal data plots of polarization attributes provide evidence for shear wave splitting in an sg arrival having determined the instantaneous polarization vector we design a new type of time domain spatial directional filter the filter enhances linearly polarized events with specified instantaneous polarization the

a higher order godunov method for modeling finite deformation in elastic plastic solids in this paper we develop a first order system of conservation laws for finite deformation in solids describe its characteristic structure and use this analysis to develop a second order numerical method for problems involving finite deformation and plasticity the equations of mass momentum and energy conservation in lagrangian and eulerian frames of reference are combined with kinetic equations of state for the stress and with caloric equations of state for the internal energy as well as with auxiliary equations representing equality of mixed partial derivatives of the deformation gradient particular attention is paid to the influence of a curl constraint on the deformation gradient so that the characteristic speeds transform properly between the two frames of reference next we consider models in rate form for isotropic elastic plastic materials with work hardening and examine the circumstances under which these models lead to hyperbolic systems for the equations of motion in spite of the fact that these models violate thermodynamic principles in such a way that the acoustic tensor becomes nonsymmetric we still find that the characteristic speeds are always real for elastic behavior and essentially always real for plastic response these results allow us to construct a second order godunov method for the computation of three dimensional displacement in a one dimensional material viewed in the lagrangian frame of reference we also describe a technique for the approximate solution of riemann problems in order to determine numerical fluxes in this algorithm finally we present numerical examples of the results of the algorithm

a high order godunov method for multiple condensed phases presented in this work is a nonlinear adaptive nonreflecting boundary condition nrbc that when compared with classical local nrbcs further reduces the wave reflection error at far fields in the numerical simulation of wave dominated problems a nonlinear procedure can considerably improve the accuracy of nrbcs even if the problem itself is linear as in the case of the 2d wave equation in fact the first and second order nrbcs of engquist and majda can be modified by adding proper weights to the coefficients of the difference equations the weights are adaptively determined in such a way that the angle of complete absorption is locally coincident with the outgoing wave direction the theoretical reflection coefficients and the numerical experiments show that a considerable reduction of the numerical error due to wave reflections is achieved by applying the present adaptive algorithm

cellwise conservative unsplit advection for the volume of fluid method we present a cellwise conservative unsplit ccu advection scheme for the volume of fluid method vof in 2d contrary to other schemes based on explicit calculations of the flux balances the ccu advection adopts a cellwise approach where the pre images of the control volumes are traced backwards through the flow map the donating regions of the fluxes are calculated via the streaklines of the grid intersections represented as polygonal chains whose vertices are determined by backward tracing of particles injected in the flow at different times high order accuracy is obtained from the fourth order runge kutta method where intermediate velocities along pathlines are determined with quadratic temporal and bicubic spatial interpolations the volumes of the donating regions are corrected in order to fulfill the discrete continuity of incompressible flows consequently the calculation produces non overlapping donating regions and pre images with conforming edges to their neighbors resulting in the conservativeness and the boundedness liquid volume fraction inside the interval 0 1 of the ccu advection scheme finally the update of the liquid volume fractions is computed from the intersections of the pre image polygons with the reconstructed interfaces the ccu scheme is tested on several benchmark tests for the vof advection together with the standard piecewise linear interface calculation plic the geometrical errors of the ccu compare favorably with other unsplit vof plic schemes finally potential improvements of the vof method with the use of more precise interface representation techniques and the future extension of the ccu scheme to 3d are discussed cellwise vof update through backward tracing of the cell s pre image accuracy enhanced via bicubic spatial interpolation and polygonal chain streakline the ccu advection scheme is fully conservative and bounded no limitation on the courant number geometrical errors dominated by plic interface representation errors

characterization of polarization attributes of seismic waves using continuous wavelet transforms complex trace analysis is the method of choice for analyzing polarized data because particle motion can be represented by instantaneous attributes that show distinct features for waves of different polarization characteristics it can be used to separate and characterize these waves traditional methods of complex trace analysis only give the instantaneous attributes as a function of time or frequency however for transient wave types or seismic events that overlap in time an estimate of the polarization parameters requires analysis of the time frequency dependence of these attributes we propose a method to map instantaneous polarization attributes of seismic signals in the wavelet domain and explicitly relate these attributes with the wavelet transform coefficients of the analyzed signal we compare our method with traditional complex trace analysis using numerical examples an advantage of our method is its possibility of performing the complete wave mode separation filtering process in the wavelet

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

a cartesian grid embedded boundary method for poisson s equation on irregular domains we present a numerical method for solving poisson s equation with variable coefficients and dirichlet boundary conditions on two dimensional regions the approach uses a finite volume discretization which embeds the domain in a regular cartesian grid we treat the solution as a cell centered quantity even when those centers are outside the domain cells that contain a portion of the domain boundary use conservative differencing of second order accurate fluxes on each cell volume the calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes this allows us to use multigrid iterations with a simple point relaxation strategy we have combined this with an adaptive mesh refinement amr procedure we provide evidence that the algorithm is second order accurate on various exact solutions and compare the adaptive and nonadaptive calculations

an eulerian algorithm for coupled simulations of elastoplastic solids and condensed phase explosives the performance of non ideal condensed phase explosives depends on the nature of the confiner material as well as the charge itself so the accurate modelling of this confiner and its interaction with the explosive allows for improved performance predictions traditionally numerical methods for solving such multi material problems have used lagrangian or mixed eulerian lagrangian approaches but recent advances in numerical methods for coupling cfd computational fluid dynamics and cmd computational material dynamics algorithms has made such coupled simulations possible in the eulerian frame of reference however to date the explosive material representation within these simulations has been restricted to the single phase euler equations in the present study we couple a multi phase chemically active model for condensed phase explosives to an elastic plastic model for inert confiner materials in the presented algorithm the ghost fluid method is employed to represent the evolving material interfaces as discontinuities on discrete space the coupling between the materials at these interfaces is achieved by means of a new approximate mixed riemann solver developed as part of this research in addition we present a mixed riemann solver for a simpler transport model which ignores compaction effects at the interface the robustness and accuracy of the developed solvers is demonstrated by comparisons against results from the original ghost fluid method and exact solutions of model riemann problems to allow for more realistic material behaviour the mixed riemann solvers are subsequently extended to handle the shock mie gruneisen equation of state and an iterative procedure is suggested to increase accuracy as required these mixed riemann solvers demonstrate their suitability for explosive solid interactions in two test cases of multi phase detonations confined by an elastic plastic solid

a finite strain eulerian formulation for compressible and nearly incompressible hyperelasticity using high order b spline finite elements summary we present a numerical formulation aimed at modeling the nonlinear response of elastic materials using large deformation continuum mechanics in three dimensions this finite element formulation is based on the eulerian description of motion and the transport of the deformation gradient when modeling a nearly incompressible solid the transport of the deformation gradient is decomposed into its isochoric part and the jacobian determinant as independent fields a homogeneous isotropic hyperelastic solid is assumed and b splines based finite elements are used for the spatial discretization a variational multiscale residual based approach is employed to stabilize the transport equations the performance of the scheme is explored for both compressible and nearly incompressible applications the numerical results are in good agreement with theory illustrating the viability of the computational scheme copyright 2011 john wiley sons ltd

discretization of hyperelasticity on unstructured mesh with a cell centered lagrangian scheme we present a new cell centered lagrangian scheme on unstructured mesh for hyperelasticity it is based on the recently proposed glace scheme 11 for compressible gas dynamics we show how to use the multiplicative decomposition of the gradient of deformation and the entropy property to derive the new scheme we also prove the compatibility of this discretization with usual calculations of mass our motivation is to use hyperelasticity models for the study of finite plasticity which is an extension of hypoelasticity to finite deformations hyperelasticity is a natural choice for extended models in solid mechanics because of its mathematical structure which is a system of conservation laws with full rotational invariance we study these properties for the lagrangian system and detail the various eulerian formulations we present several test problems in 1d and 2d planar cases which shows the capability of the scheme to capture complex shock waves and to simulate solid fluid problems in this article we use a special equation of state 21 its interest is twofold we can calculate multi dimensional plastic phenomenon such as split shock in 1d uniaxial cases or particular shapes in taylor test case and it gives interesting multi dimensional test cases for hyperelastic planar schemes

modelling wave dynamics of compressible elastic materials an eulerian conservative hyperbolic model of isotropic elastic materials subjected to finite deformation is addressed it was developed by godunov s k godunov elements of continuum mechanics nauka moscow 1978 in russian and g h miller p colella a high order eulerian godunov method for elastic plastic flow in solids j comput phys 167 2001 131 176 some modifications are made concerning a more suitable form of governing equations they form a set of evolution equations for a local cobasis which is naturally related to the almansi deformation tensor another novelty is that the equation of state is given in terms of invariants of the almansi tensor in a form which separates hydrodynamic and shear effects this model is compared with another hyperbolic non conservative model which is widely used in engineering sciences for this model we develop a riemann solver and determine some reference solutions which are compared with the conservative model the numerical results for different tests show good agreement of both models for waves of very small and very large amplitude however for waves of intermediate amplitude important discrepancies between results are clearly visible

a newton krylov solver for remapping based volume of fluid methods a new conservative remapping method is presented here for generating multi dimensional fluxes used for the time integration of hyperbolic equations through single stage unsplit advection a solution to the lagrangian mesh location is generated that converges the volumes of all remapped flux definitions to the volumes of equivalent one dimensional flux definitions at their corresponding cell faces the method is most feasible within localized subdomains of an eulerian solution domain the main utility of the method is the generation of fluxes in the vicinity of discontinuities and sharp gradients that does not introduce physically spuriously extrema while locally conserving mass in generating solutions to lagrangian mesh location by solving a nonlinear equation system the new remap requires the anchoring of the lagrangian mesh removal of degrees of freedom to make the problem definite the method is based on characteristic tracing along trajectories assumed to be linear this paper investigates the convergence and sensitivity of the lagrangian mesh solver to mesh and timestep size in assessing its merit for application in transient cfd codes for single stage unsplit advection volume of fluid methods the new remap suppresses the introduction of undershoots overshoots and wisps in combination with a conservative remapping phase the new method for fixing the location of the lagrangian mesh eliminates the need for heuristic redistribution or clipping procedures for spurious extrema removal

effects of element distortions on the performance of isoparametric elements we discuss the effects of element distortions on the performance of displacement based isoparametric quadrilateral finite elements suitable example problems for both the lagrangian and the serendipity types of elements are used to show numerically the effects of element distortions the effects of angular and curved edge distortions are evaluated analytically in terms of the abilities of the elements to represent exactly various polynomial displacement fields we then solve a plane stress problem adaptively to demonstrate the effect of element distortions on the accuracy of the stress distribution the conclusion is that the lagrangian elements are not affected by angular distortions and are therefore the more reliable elements for general use

a fast pressure correction method for incompressible two fluid flows we have developed a new pressure correction method for simulating incompressible two fluid flows with large density and viscosity ratios the method s main advantage is that the variable coefficient poisson equation that arises in solving the incompressible navier stokes equations for two fluid flows is reduced to a constant coefficient equation which can be solved with an fft based fast poisson solver this reduction is achieved by splitting the variable density pressure gradient term in the governing equations the validity of this splitting is demonstrated from our numerical tests and it is explained from a physical viewpoint in this paper the new pressure correction method is coupled with a mass conserving volume of fluid method to capture the motion of the interface between the two fluids but in general it could be coupled with other interface advection methods such as level set phase field or front tracking first we verified the new pressure correction method using the capillary wave test case up to density and viscosity ratios of 10 000 then we validated the method by simulating the motion of a falling water droplet in air and comparing the droplet terminal velocity with an experimental value next the method is shown to be second order accurate in space and time independent of the vof method and it conserves mass momentum and kinetic energy in the inviscid limit also we show that for solving the two fluid navier stokes equations the method is 10 40 times faster than the standard pressure correction method which uses multigrid to solve the variable coefficient poisson equation finally we show that the method is capable of performing fully resolved direct numerical simulation dns of droplet laden isotropic turbulence with thousands of droplets using a computational mesh of 1024 3 points

an unsplit 3d upwind method for hyperbolic conservation laws abstract an unsplit upwind method for solving hyperbolic conservation laws in three dimensions is developed this paper derives the algorithm by generalizing a two dimensional advection algorithm of van leer and colella to three dimensions and then making appropriate modifications the method is implemented using the equations of gas dynamics several test problems are computed to both verify and display the behavior of the method these test problems include a 1d blast wave a 2d shock reflection off a 30 ramp and a 3d astrophysical jet

deforming composite grids for solving fluid structure problems we describe a mixed eulerian lagrangian approach for solving fluid structure interaction fsi problems the technique which uses deforming composite grids dcg is applied to fsi problems that couple high speed compressible flow with elastic solids the fluid and solid domains are discretized with composite overlapping grids curvilinear grids are aligned with each interface and these grids deform as the interface evolves the majority of grid points in the fluid domain generally belong to background cartesian grids which do not move during a simulation the fsi dcg approach allows large displacements of the interfaces while retaining high quality grids efficiency is obtained through the use of structured grids and cartesian grids the governing equations in the fluid and solid domains are evolved in a partitioned approach we solve the compressible euler equations in the fluid domains using a high order godunov finite volume scheme we solve the linear elastodynamic equations in the solid domains using a second order upwind scheme we develop interface approximations based on the solution of a fluid solid riemann problem that results in a stable scheme even for the difficult case of light solids coupled to heavy fluids the fsi dcg approach is verified for three problems with known solutions an elastic piston problem the superseismic shock problem and a deforming diffuser in addition a self convergence study is performed for an elastic shock hitting a fluid filled cavity the overall fsi dcg scheme is shown to be second order accurate in the max norm for smooth solutions and robust and stable for problems with discontinuous solutions for a wide range of constitutive parameters

an added mass partition algorithm for fluid structure interactions of compressible fluids and nonlinear solids we describe an added mass partitioned amp algorithm for solving fluid structure interaction fsi problems involving inviscid compressible fluids interacting with nonlinear solids that undergo large rotations and displacements the computational approach is a mixed eulerian lagrangian scheme that makes use of deforming composite grids dcg to treat large changes in the geometry in an accurate flexible and robust manner the current work extends the amp algorithm developed in banks et al 1 for linearly elasticity to the case of nonlinear solids to ensure stability for the case of light solids the new amp algorithm embeds an approximate solution of a nonlinear fluid solid riemann fsr problem into the interface treatment the solution to the fsr problem is derived and shown to be of a similar form to that derived for linear solids the state on the interface being fundamentally an impedance weighted average of the fluid and solid states numerical simulations demonstrate that the amp algorithm is stable even for light solids when added mass effects are large the accuracy and stability of the amp scheme is verified by comparison to an exact solution using the method of analytical solutions and to a semi analytical solution that is obtained for a rotating solid disk immersed in a fluid the scheme is applied to the simulation of a planar shock impacting a light elliptical shaped solid and comparisons are made between solutions of the fsi problem for a neo hookean solid a linearly elastic solid and a rigid solid the ability of the approach to handle large deformations is demonstrated for a problem of a high speed flow past a light thin and flexible solid beam

an iterative riemann solver for systems of hyperbolic conservation laws with application to hyperelastic solid mechanics in this paper we present a general iterative method for the solution of the riemann problem for hyperbolic systems of pdes the method is based on the multiple shooting method for free boundary value problems we demonstrate the method by solving one dimensional riemann problems for hyperelastic solid mechanics even for conditions representative of routine laboratory conditions and military ballistics dramatic differences are seen between the exact and approximate riemann solution the greatest discrepancy arises from misallocation of energy between compressional and thermal modes by the approximate solver resulting in nonphysical entropy and temperature estimates several pathological conditions arise in common practice and modifications to the method to handle these are discussed these include points where genuine nonlinearity is lost degeneracies and eigenvector deficiencies that occur upon melting

three dimensional adaptive mesh refinement for hyperbolic conservation laws a local adaptive mesh refinement algorithm for solving hyperbolic systems of conservation laws in three space dimensions is described the method is based on the use of local grid patches superimpo

a three dimensional unsplit godunov method for scalar conservation laws linear advection of a scalar quantity by a specified velocity field arises in a number of different applications of particular interest here is the transport of species and energy in low mach number models for combustion atmospheric flows and astrophysics as well as contaminant transport in darcy models of saturated subsurface flow an important characteristic of these problems is that the velocity field is not known analytically instead an auxiliary equation is solved to compute averages of the velocities over faces in a finite volume discretization in this paper we present a customized three dimensional finite volume advection scheme for this class of problems that provides accurate resolution for smooth problems while avoiding undershoot and overshoot for nonsmooth profiles the method is an extension of an algorithm by bell dawson and shubin bds which was developed for a class of scalar conservation laws arising in porous media flows in two dimensions the original bds algorithm is a variant of unsplit higher order godunov methods based on construction of a limited bilinear profile within each computational cell here we present a three dimensional extension of the original bds algorithm that is based on a limited trilinear profile within each cell we compare this new method to several other unsplit approaches including piecewise linear methods piecewise parabolic methods and wave propagation schemes

new superconvergent points of the 8 node serendipity plane element for patch recovery the gaussian quadrature points which are generally observed to be the same as the barlow points for lower order elements have so far been used as the sampling points for the superconvergent patch recovery spr recent developments on the best fit method to calculate the optimal sampling points suggest that for higher order elements barlow points need not be the optimal sampling points and also need not be the same as the gaussian quadrature points in this paper the best fit method is extended to predict the optimal points of the 8 node serendipity rectangular element and it is observed that best fit points do not exist next a novel method is proposed in which the expressions for stress error based on the best fit are used in the least square fit of the patch recovery and thereby the superconvergent points are obtained more directly application of this method to the 8 node serendipity element reveals the existence of two sets of superconvergent points for patch recovery one of which is the well known gaussian points and the other is the set of four points given by the existence of which has not been known before a detailed numerical study on the patch recovery of stresses for two demonstrative problems reveals that there indeed exist two sets of superconvergent points as predicted by the proposed method the comparative performance of the two sets of points is tested for typical demonstrative problems and the results are discussed copyright 2002 john wiley sons ltd

an unsplit godunov method for ideal mhd via constrained transport we describe a single step second order accurate godunov scheme for ideal mhd based on combining the piecewise parabolic method ppm for performing spatial reconstruction the corner transport upwind ctu method of colella for multidimensional integration and the constrained transport ct algorithm for preserving the divergence free constraint on the magnetic field we adopt the most compact form of ct which requires the field be represented by area averages at cell faces we demonstrate that the fluxes of the area averaged field used by ct can be made consistent with the fluxes of the volume averaged field returned by a riemann solver if they obey certain simple relationships we use these relationships to derive new algorithms for constructing the ct fluxes at grid cell corners which reduce exactly to the equivalent one dimensional solver for plane parallel grid aligned flow we show that the ppm reconstruction algorithm must include multidimensional terms for mhd and we describe a number of important extensions that must be made to ctu in order for it to be used for mhd with ct we present the results of a variety of test problems to demonstrate the method is accurate and robust

solid fluid diffuse interface model in cases of extreme deformations diffuse interface methods have been recently proposed and successfully used for accurate compressible multi fluid computations abgrall 1 kapila et al 20 saurel et al 30 these methods deal with extended systems of hyperbolic equations involving a non conservative volume fraction equation and relaxation terms following the same theoretical frame we derive here an eulerian diffuse interface model for elastic solid compressible fluid interactions in situations involving extreme deformations elastic effects are included following the eulerian conservative formulation proposed in godunov 16 miller and colella 23 godunov and romenskii 17 plohr and plohr 27 and gavrilyuk et al 14 we apply first the hamilton principle of stationary action to derive the conservative part of the model the relaxation terms are then added which are compatible with the entropy inequality in the limit of vanishing volume fractions the euler equations of compressible fluids and a conservative hyperelastic model are recovered it is solved by a unique hyperbolic solver valid at each mesh point pure fluid pure solid and mixture cell capabilities of the model and methods are illustrated on various tests of impacts of solids moving in an ambient compressible fluid

instantaneous polarization attributes based on an adaptive approximate covariance method we introduce a method for computing instantaneous polarization attributes from multicomponent signals this is an improvement on the standard covariance method scm because it does not depend on the window size used to compute the standard covariance matrix we overcome the window size problem by deriving an approximate analytical formula for the cross energy matrix in which we automatically and adaptively determine the time window the proposed method uses polarization analysis as applied to multicomponent seismic by waveform separation and filtering

an unsplit godunov method for ideal mhd via constrained transport in three dimensions we present a single step second order accurate godunov scheme for ideal mhd which is an extension of the method described in t a gardiner j m stone an unsplit godunov method for ideal mhd via constrained transport j comput phys 205 2005 509 to three dimensions this algorithm combines the corner transport upwind ctu method of colella for multidimensional integration and the constrained transport ct algorithm for preserving the divergence free constraint on the magnetic field we describe the calculation of the ppm interface states for 3d ideal mhd which must include multidimensional mhd source terms and naturally respect the balance implicit in these terms by the b 0 condition we compare two different forms for the ctu integration algorithm which require either 6 or 12 solutions of the riemann problem per cell per time step and present a detailed description of the 6 solve algorithm finally we present solutions for test problems to demonstrate the accuracy and robustness of the algorithm