a comparative study of different sets of variables for solving compressible and incompressible flows a globally conservative galerkin least squares formulation which attains correct shock structure is developed for any choice of variables only the choice of entropy variables satisfies exactly the discrete clausius duhem inequality without any dissipative mechanisms whereas for the rest of the variables artificial diffusion is required to guarantee entropy production the limit of the formulation is well defined for entropy variables and the primitive variables p u t leading to conservative incompressible formulations the approach is stable for any continuous interpolations both for compressible and incompressible flows a comparative study of different variables is performed indicating that entropy variables and the primitive variables p u t possess the most attributes for practical problem solving

a symmetric formulation for computing transient shallow water flows abstract the shallow water equations fall into the category of symmetric advective diffusive systems with source terms these types of equations can be very effectively solved using stabilized methods such as supg and gls a semi discrete finite element method based on these ingredients is presented for the computation of transient shallow water flows special care has been taken in the design of the operators in order to improve the performance for unsteady calculations the solution is advanced in time via a predictor multi corrector algorithm which includes as special cases the second order trapezoidal rule a first order explicit method and a first order implicit method equivalent to the constant in time element of the space time formulation

a conservative formulation of the multidimensional upwind residual distribution schemes for general nonlinear conservation laws in the present paper we consider the numerical solution of systems of general nonlinear hyperbolic conservation laws on unstructured grids by means of the residual distribution method we propose a new formulation of the first order linear optimal positive n scheme relying on a contour integration of the convective fluxes over the boundaries of an element full conservation is achieved for arbitrary flux functions while the robustness and the monotone shock capturing of the original n scheme is retained the new variant of the n scheme is combined with the conservative second order linear lda scheme to obtain a nonlinear second order monotone b scheme the performance of the new residual distribution schemes is evaluated on problems governed by the euler equations as an application to a more complex system of conservation laws lacking an exact conservative linearization we solve the ideal magnetohydrodynamics equations in two spatial dimensions

the cauchy problem associated to the benjamin equation in weighted sobolev spaces abstract we study the initial value problem associated to the benjamin equation our purpose here is to establish persistence properties and some unique continuation properties of the solutions of this equation in weighted sobolev spaces

second order blended multidimensional upwind residual distribution scheme for steady and unsteady computations multidimensional upwind residual distribution rd schemes have become an appealing alternative to more widespread finite volume and finite element methods fem for solving compressible fluid flows the rd approach allows to construct nonlinear second order and non oscillatory methods at the same time they are routinely used for steady state calculations of the complex flow problems e g 3d turbulent transonic industrial type simulations h deconinck k sermeus r abgrall status of multidimensional upwind residual distribution schemes and applications in aeronautics aaia paper 2000 2328 aiaa 2000 k sermeus h deconinck drag prediction validation of a multi dimensional upwind solver cfd based aircraft drag prediction and reduction vki lecture series 2003 02 von karman institute for fluid dynamics chausee do waterloo 72 b 1640 rhode saint genese belgium 2003 despite its maturity some problems are still present for the nonlinear schemes developed up to now namely a poor iterative convergence for the transonic problems and a decrease of accuracy in smooth parts of the flow caused by a weak l 2 instability m ricchiuto construction and analysis of compact residual discretizations for conservation laws on unstructured meshes ph d thesis universite libre de bruxelles von karman institute for fluid dynamics 2005 we have developed a new formulation of a blended scheme between the second order linear lda r abgrall m mezine residual distribution scheme for steady problems 33rd computational fluid dynamics course vki lecture series 2003 05 von karman institute for fluid dynamics chausee do waterloo 72 b 1640 rhode saint genese belgium 2003 scheme and the first order n scheme the blending coefficient is based on a simple shock capturing operator and it is properly scaled such that second order accuracy is preserved the approach is extended to unsteady flows problems using consistent formulation of the lda scheme with the mass matrix m mezine m ricchiuto r abgrall h deconinck monotone and stable residual distribution schemes on prismatic space time elements for unsteady conservation laws 33rd computational fluid dynamics course von karman institute for fluid dynamics 2003 r abgrall m mezine construction of second order accurate monotone and stable residual distribution schemes for unsteady flow problems j comput phys 188 2003 16 55 for the time integration a three point backward scheme is selected for its accuracy and robustness and the shock capturing operator is modified appropriately to handle moving shocks we present a numerical solution of several challenging test cases involving the solution of the euler equations from the subsonic to the hypersonic regime all the tests shows very good accuracy robustness and convergence properties

a second order accurate monotone implicit fluctuation splitting scheme for unsteady problems this paper provides an implicit fluctuation splitting scheme which achieves second order accuracy in both space and time while guaranteeing monotone solutions the method is based on a dual time stepping approach which allows to separate the spatial and temporal discretizations a novel distribution scheme of the unsteady fluctuation term coupled with a new limiting procedure for hampering spurious extrema are the key ingredients of the remarkable accuracy of the new method which is applied with success to both scalar advection problems and unsteady inviscid flows in two space dimensions

the ivp for a nonlocal perturbation of the benjamin ono equation in classical and weighted sobolev spaces abstract we prove that the initial value problem associated to a nonlocal perturbation of the benjamin ono equation is locally and globally well posed in sobolev spaces h s r for any s 3 2 and we establish that our result is sharp in the sense that the flow map of this equation fails to be c 2 in h s r for s 3 2 finally we study persistence properties of the solution flow in the weighted sobolev spaces z s r h s r l 2 x 2 r d x for s r 0 we also prove some unique continuation properties of the solution flow in these spaces

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

third order accurate fluctuation splitting schemes for unsteady hyperbolic problems this paper provides a two dimensional fluctuation splitting scheme for unsteady hyperbolic problems which achieves third order accuracy in both space and time for a scalar conservation law the sufficient conditions for a stable fluctuation splitting scheme to achieve a prescribed order of accuracy in both space and time are derived then using a quadratic space approximation of the solution over each triangular element based on the reconstruction of the gradient at the three vertices and a four level backward discretization of the time derivative an implicit third order accurate scheme is designed such a scheme is extended to the euler system and is validated versus well known scalar advection problems and inviscid discontinuous flows

supg finite element computation of compressible flows with the entropy and conservation variables formulations abstract supg stabilized finite element formulations of compressible euler equations based on the conservation and entropy variables are investigated and compared the formulation based on the conservation variables consists of the formulation introduced by tezduyar and hughes plus a shock capturing term the formulation based on the entropy variables is the same as the one by hughes franca and mallet which has a shock capturing term built in these formulations are tested on several subsonic transonic and supersonic compressible flow problems it is shown that the stabilized formulation based on the conservation variables gives solutions which are just as good as those obtained with the entropy variables furthermore the solutions obtained using the two formulations are very close and in some cases almost indistinguishable consequently it can be deduced that the relative merits of these two formulations will continue to remain under debate

higher order triangular finite elements with mass lumping for the wave equation in this article we construct new higher order finite element spaces for the approximation of the two dimensional 2d wave equation these elements lead to explicit methods after time discretization through the use of appropriate quadrature formulas which permit mass lumping these formulas are constructed explicitly error estimates are provided for the corresponding semidiscrete problem finally higher order finite difference time discretizations are proposed and various numerical results are shown

simple stabilizing matrices for the computation of compressible flows in primitive variables the key ingredient that balances stability and accuracy in stabilized formulations is the parameter of intrinsic time scales for multi dimensional hyperbolic systems of equations this parameter is a matrix and the available expressions for its computation involve the solution of an eigenvalue problem which can be tedious or cpu time consuming thus for formulations based on primitive variables including pressure a couple of simple stabilizing matrices are presented which are easy to implement and cpu economic numerical evaluations show the performance of the various choices

stability of the supg finite element method for transient advection diffusion problems implicit time integration coupled with supg discretization in space leads to additional terms that provide consistency and improve the phase accuracy for convection dominated flows recently it has been suggested that for small courant numbers these terms may dominate the streamline diffusion term ostensibly causing destabilization of the supg method while consistent with a straightforward finite element stability analysis this contention is not supported by computational experiments and contradicts earlier von neumann stability analyses of the semidiscrete supg equations this prompts us to re examine finite element stability of the fully discrete supg equations a careful analysis of the additional terms reveals that regardless of the time step size they are always dominated by the consistent mass matrix consequently supg cannot be destabilized for small courant numbers numerical results that illustrate our conclusions are reported

on the symmetric form of systems of conservation laws with entropy abstract this paper reviews the symmetrizability of systems of conservation laws which possess entropy functions symmetric formulations in conservation form for the equations of gas dynamics are presented

space time residual distribution on moving meshes abstract this article investigates the potential for an r adaptation algorithm to improve the efficiency of space time residual distribution schemes in the approximation of time dependent hyperbolic conservation laws e g scalar advection shallow water flows on unstructured triangular meshes in this adaptive framework the connectivity of the mesh and hence the number of degrees of freedom remain fixed but the mesh nodes are continually relocated as the flow evolves so that features of interest remain resolved as they move within the domain adaptive strategies of this type are well suited to the space time residual distribution framework because when the discrete representation is allowed to be discontinuous in time these algorithms can be designed to be positive and hence stable for any choice of time step even on the distorted space time prisms which arise from moving the nodes of an unstructured triangular mesh consequently a local increase in mesh resolution does not impose a more restrictive stability constraint on the time step which can instead be chosen according to accuracy requirements the order of accuracy of the fixed mesh scheme is retained on the moving mesh in the majority of applications tested space time schemes of this type are analogous to conservative ale formulations and automatically satisfy a discrete geometric conservation law so moving the mesh does not artificially change the flow volume for pure conservation laws for shallow water flows over variable bed topography the so called c property retention of hydrostatic balance between flux and source terms required to maintain the steady state of still flat water can also be satisfied by considering the mass balance equation in terms of free surface level instead of water depth even when the mesh is moved the r adaptation is applied within each time step by interleaving the iterations of the nonlinear solver with updates to mesh node positions the node movement is driven by a monitor function based on weighted approximations of the scaled gradient and laplacian of the local solution and regularised by a smoothing iteration numerical results are shown in two dimensions for both scalar advection and for shallow water flow over a variable bed which show that even for this simple implementation of the mesh movement reductions in cpu times of up to 60 can be attained without increasing the error

upwind residual discretization of enhanced boussinesq equations for wave propagation over complex bathymetries in this paper we consider the solution of the enhanced boussinesq equations of madsen and sorensen 1992 55 by means of residual based discretizations in particular we investigate the applicability of upwind and stabilized variants of continuous galerkin finite element and residual distribution schemes for the simulation of wave propagation and transformation over complex bathymetries these techniques have been successfully applied to the solution of the nonlinear shallow water equations see e g hauke 1998 39 and ricchiuto and bollermann 2009 61 in a first step toward the construction of a hybrid model coupling the enhanced boussinesq equations with the shallow water equations in breaking regions this paper shows that equal order and even low order second upwind stabilized techniques can be used to model non hydrostatic wave propagation over complex bathymetries this result is supported by theoretical truncation and dispersion error analyses and by thorough numerical validation

stabilized residual distribution for shallow water simulations we propose a stabilized residual distribution rd scheme for the simulation of shallow water flows the final discretization is obtained combining the stabilized rd approach proposed in abgrall j comp phys 214 2006 and ricchiuto and abgrall iccfd4 springer verlag 2006 with the conservative formulation already used in ricchiuto et al j comp phys 222 2007 to simulate shallow water flows the scheme proposed is a nonlinear variant of a lax friedrichs type discretization it is well balanced it actually yields second order of accuracy in smooth areas and it preserves the positivity of the height of the water in presence of dry areas this is made possible by the residual character of the discretization by properly adapting the stabilization operators proposed in abgrall j comp phys 214 2006 and ricchiuto and abgrall iccfd4 springer verlag 2006 and thanks to the positivity preserving character of the underlying lax friedrichs scheme we demonstrate the properties of the discretization proposed on a wide variety of tests

the ivp for the benjamin ono zakharov kuznetsov equation in low regularity sobolev spaces abstract in this paper we study the initial value problem associated with the benjamin ono zakharov kuznetsov equation such equation appears as a two dimensional generalization of the benjamin ono equation when transverse effects are included via weak dispersion of zakharov kuznetsov type we prove that the initial value problem is locally well posed in the usual l 2 r 2 based sobolev spaces h s r 2 s 11 8 and in some weighted sobolev spaces to obtain our results most of the arguments are accomplished taking into account the ones for the benjamin ono equation

hammer hierarchical attribute matching mechanism for elastic registration a new approach is presented for elastic registration of medical images and is applied to magnetic resonance images of the brain experimental results demonstrate very high accuracy in superposition of images from different subjects there are two major novelties in the proposed algorithm first it uses an attribute vector i e a set of geometric moment invariants gmis that are defined on each voxel in an image and are calculated from the tissue maps to reflect the underlying anatomy at different scales the attribute vector if rich enough can distinguish between different parts of an image which helps establish anatomical correspondences in the deformation procedure it also helps reduce local minima by reducing ambiguity in potential matches this is a fundamental deviation of our method referred to as the hierarchical attribute matching mechanism for elastic registration hammer from other volumetric deformation methods which are typically based on maximizing image similarity second in order to avoid being trapped by local minima i e suboptimal poor matches hammer uses a successive approximation of the energy function being optimized by lower dimensional smooth energy functions which are constructed to have significantly fewer local minima this is achieved by hierarchically selecting the driving features that have distinct attribute vectors thus drastically reducing ambiguity in finding correspondence a number of experiments demonstrate that the proposed algorithm results in accurate superposition of image data from individuals with significant anatomical differences

synthesizing average 3d anatomical shapes abstract average shape estimates are often used to characterize normal morphological variation and discriminate dysmorphology in populations the purpose of this paper is to estimate average or the most representative shapes in populations by using high resolution medical images as input the average shape is computed from high dimensional spatial transformations used to co register each subject in the population rather than the image intensities inverse consistent image registration is used to help minimize correspondence errors and produce better population average estimates testing the method was done using a population of adult mr brain scans from 22 individuals with no know structural abnormalities population averages were computed using the spatial transformation method and local changes in morphology were mapped results suggest that this method is a feasible means for robust estimation of population average shape it is also shown that using inverse consistent transformations produces average shape estimates with less error compared to those produced with transformations with nontrivial inverse consistent errors

implicit reference based group wise image registration and its application to structural and functional mri abstract in this study an implicit reference group wise irg registration with a small deformation linear elastic model was used to jointly estimate correspondences between a set of mri images the performance of pair wise and group wise registration algorithms was evaluated for spatial normalization of structural and functional mri data traditional spatial normalization is accomplished by group to reference g2r registration in which a group of images are registered pair wise to a reference image g2r registration is limited due to bias associated with selecting a reference image in contrast implicit reference group wise irg registration estimates correspondences between a group of images by jointly registering the images to an implicit reference corresponding to the group average the implicit reference is estimated during irg registration eliminating the bias associated with selecting a specific reference image registration performance was evaluated using segmented t1 weighted magnetic resonance images from the nonrigid image registration evaluation project nirep dti and fmri images implicit reference pair wise irp registration a special case of irg registration for two images is shown to produce better relative overlap than irg for pair wise registration using the same small deformation linear elastic registration model however irp g2r registration is shown to have significant transitivity error i e significant inconsistencies between correspondences defined by different pair wise transformations in contrast irg registration produces consistent correspondence between images in a group at the cost of slightly reduced pair wise ro accuracy compared to irp g2r irg spatial normalization of the fractional anisotropy fa maps of dti is shown to have smaller fa variance compared with g2r methods using the same elastic registration model analyses of fmri data sets with sensorimotor and visual tasks show that irg registration on average increases the statistical detectability of brain activation compared to g2r registration

an explicit residual based approach for shallow water flows we describe fully explicit residual based discretizations of the shallow water equations with friction on unstructured grids the schemes are obtained by properly adapting the explicit construction proposed in ricchiuto and abgrall 2010 57 in particular previous work on well balanced integration ricchiuto 2011 56 and preservation of the depth non negativity ricchiuto and bollermann 2009 60 is reformulated in the context of a genuinely explicit time stepping still based on a weighted residual approximation the paper discusses in depth how to achieve in this context an exact preservation of all the simple known steady equilibria and how to obtain a super consistent approximation for smooth non trivial moving equilibria the treatment of the wetting drying interface is also discussed giving formal conditions for the preservation of the non negativity of the depth for a particular case based on a nonlinear variant of a lax friedrichs type scheme the approach is analyzed and tested thoroughly the quality of the numerical results shows the interest in the proposed approach over previously proposed schemes in terms of accuracy and efficiency

the cauchy problem for dissipative benjamin ono equation in weighted sobolev spaces abstract we study the well posedness in weighted sobolev spaces for the initial value problem ivp associated with the dissipative benjamin ono dbo equation we establish persistence properties of the solution flow in the weighted sobolev spaces z s r h s r l 2 x 2 r d x s r 0 we also prove some unique continuation properties in these spaces in particular such results of unique continuation show that our results of well posedness are sharp

on uniformly high order accurate residual distribution schemes for advection diffusion we discuss preliminary results on the construction of uniformly high order residual distribution rd type discretizations for steady advection diffusion on unstructured grids a properly designed scaling of the rd upwind stabilization with the physical viscosity allows to obtain schemes with uniform and arbitrary accuracy on a very compact stencil second and third order examples are given to illustrate the potential of the approach

consistent image registration presents a new method for image registration based on jointly estimating the forward and reverse transformations between two images while constraining these transforms to be inverses of one another this approach produces a consistent set of transformations that have less pairwise registration error i e better correspondence than traditional methods that estimate the forward and reverse transformations independently the transformations are estimated iteratively and are restricted to preserve topology by constraining them to obey the laws of continuum mechanics the transformations are parameterized by a fourier series to diagonalize the covariance structure imposed by the continuum mechanics constraints and to provide a computationally efficient numerical implementation results using a linear elastic material constraint are presented using both magnetic resonance and x ray computed tomography image data the results show that the joint estimation of a consistent set of forward and reverse transformations constrained by linear elasticity give better registration results than using either constraint alone or none at all

application of conservative residual distribution schemes to the solution of the shallow water equations on unstructured meshes we consider the numerical solution of the shallow water equations on unstructured grids we focus on flows over wet areas the extension to the case of dry bed will be reported elsewhere the shallow water equations fall into the category of systems of conservation laws which can be symmetrized thanks to the existence of a mathematical entropy coinciding in this case with the total energy our aim is to show the application of a particular class of conservative residual distribution rd schemes to the discretization of the shallow water equations and to analyze their discrete accuracy and stability properties we give a review of conservative rd schemes showing relations between different approaches previously published and recall l stability and accuracy criteria characterizing the schemes in particular the accuracy of the rd method in presence of source terms is analyzed and conditions to construct rth order discretizations on irregular triangular grids are proved it is shown that the rd approach gives a natural way of obtaining high order discretizations which moreover preserves exactly the steady lake at rest solution independently on mesh topology nature of the variation of the bottom and polynomial order of interpolation used for the unknowns we also consider more general analytical solutions which are less investigated from the numerical view point on irregular grids linearity preserving rd schemes yield a truly second order approximation we also sketch a strategy to achieve discretizations which preserve exactly some of these solutions numerical results on steady and time dependent problems involving smooth and non smooth variations of the bottom topology show very promising features of the approach

the benjamin ono equation in weighted sobolev spaces abstract in this paper we continue the study of the initial value problem t u x u 2 2 x u u 0 in the spaces y s h s r l 2 r where 0 s 3 2 and l r 2 r denotes the set of all complex valued measurable functions such that f r 2 r 1 x 2 r f x 2 dx our main result is the proof of well posedness of the aforementioned problem in y 2 0 1 the proof involves parabolic regularization the riesz thorin interpolation theorem and kato s theory of linear evolution equations of hyperbolic type

deformable templates using large deformation kinematics a general automatic approach is presented for accommodating local shape variation when mapping a two dimensional 2 d or three dimensional 3 d template image into alignment with a topologically similar target image local shape variability is accommodated by applying a vector field transformation to the underlying material coordinate system of the template while constraining the transformation to be smooth globally positive definite jacobian smoothness is guaranteed without specifically penalizing large magnitude deformations of small subvolumes by constraining the transformation on the basis of a stokesian limit of the fluid dynamical navier stokes equations this differs fundamentally from quadratic penalty methods such as those based on linearized elasticity or thin plate splines in that stress restraining the motion relaxes over time allowing large magnitude deformations kinematic nonlinearities are inherently necessary to maintain continuity of structures during large magnitude deformations and are included in all results after initial global registration final mappings are obtained by numerically solving a set of nonlinear partial differential equations associated with the constrained optimization problem automatic regridding is performed by propagating templates as the nonlinear transformations evaluated on a finite lattice become singular application of the method to intersubject registration of neuroanatomical structures illustrates the ability to account for local anatomical variability

an adaptive residual based splitting approach for the penalized navier stokes equations the interest on immersed boundary methods ibm is increasing in computational fluid dynamics as they simplify the mesh generation problem in this work we consider an approach based on the addition of a penalty term to the navier stokes equations to account for the wall boundary conditions to discretize the resulting equations we use a residual distribution approach previously developed by some of the authors to adapt the method to the ibm considered we developed a new formulation of residual distribution based on a strang splitting method in time coupling an implicit asymptotic integration procedure of the penalization ode with a simplified explicit residual distribution for the navier stokes equations the first method provides an operator which is exact up to orders 2 with the penalty parameter assuming values of the order of 10 10 a modification of the solution gradient reconstruction necessary for the evaluation of the viscous fluxes is also introduced in the paper this guarantees that correct physical values of the viscous stresses are recovered in vicinity of the solid we show formally and numerically that the approach proposed is second order accurate for smooth solutions we evaluate its potential for ibm by coupling the resulting method with unstructured mesh adaptation on wall boundaries several steady and time dependent tests are used to show the promising features of the method proposed

staggered grid residual distribution scheme for lagrangian hydrodynamics this paper is focused on the residual distribution rd interpretation of the dobrev kolev and rieben scheme siam j sci comput 34 2012 pp b606 b641 for the numerical solution of the euler equations in lagrangian form the first ingredient of the original scheme is the staggered grid formulation which uses continuous node based finite element approximations for the kinematic variables and cell centered discontinuous finite elements for the thermodynamic parameters the second ingredient of the dobrev et al scheme is an artificial viscosity technique applied in order to make possible the computation of strong discontinuities the aim of this paper is to provide an efficient mass matrix diagonalization method in order to avoid the inversion of the global sparse mass matrix while keeping all the accuracy properties and to construct a parameter free stabilization of the scheme to get rid of the artificial viscosity in addition we study the conservation and entropy properties of the constructed

the ivp for the benjamin ono zakharov kuznetsov equation in weighted sobolev spaces abstract in this paper we study the initial value problem associated with the benjamin ono zakharov kuznetsov equation we prove that the ivp for such equation is locally well posed in the usual sobolev spaces h s r 2 s 2 and in the anisotropic spaces h s 1 s 2 r 2 s 2 2 s 1 s 2 we also study the persistence properties of the solution and local well posedness in the weighted sobolev class z s r h s r 2 l 2 1 x 2 y 2 r d x d y where s 2 r 0 and s 2 r unique continuation properties of the solution are also established these continuation principles show that our persistence properties are sharp

the ivp for a higher dimensional version of the benjamin ono equation in weighted sobolev spaces abstract we study the initial value problem associated to a higher dimensional version of the benjamin ono equation our purpose is to establish local well posedness results in weighted sobolev spaces and to determinate according to them some sharp unique continuation properties of the solution flow in consequence optimal decay rate for this model is determined a key ingredient is the deduction of a new commutator estimate involving riesz transforms

construction of stabilization operators for galerkin least squares discretizations of compressible and incompressible flows the design and analysis of a class of stabilization operators suitable for space time galerkin least squares finite element discretizations of the symmetrized compressible navier stokes equations is discussed the obtained stabilization matrix is well defined in the incompressible limit and reduces to the matrix described in m polner j j w van der vegt and r m j van damme analysis of stabilization operators for galerkin least squares discretizations of the incompressible navier stokes equations comput meth appl mech eng 195 2006 982 1006 the stabilization matrix is investigated to give necessary and sufficient conditions for its positive definiteness under these conditions on the stabilization matrix the galerkin least squares method for the symmetrized compressible navier stokes equations satisfies the entropy condition which ensures global nonlinear stability of the discretization

explicit runge kutta residual distribution schemes for time dependent problems second order case in this paper we construct spatially consistent explicit second order discretizations for time dependent hyperbolic problems starting from a given residual distribution rd discrete approximation of the steady operator we review the existing knowledge on consistent rd mass matrices and highlight the relations between different definitions we then introduce our explicit approach which is based on three main ingredients first recast the rd discretization as a stabilized galerkin scheme then use a shifted time discretization in the stabilization operator and lastly apply high order mass lumping on the galerkin component of the discretization the discussion is particularly relevant for schemes of the residual distribution type 18 3 which we will use for all our numerical experiments however similar ideas can be used in the context of residual based finite volume discretizations such as the ones proposed in 14 12 the schemes are tested on a wide variety of classical problems confirming the theoretical expectations

instability of solitary wave solutions for the generalized bo zk equation in this paper we study the generalized bo zk equation in two space dimensions ut upux huxx euxyy 0 we review the existence theory for solitary waves and prove that they are nonlinearly unstable if p belongs to the range 4 3 p 4 we also establish strichartz type estimates

fourier analysis of semi discrete and space time stabilized methods for the advective diffusive reactive equation i supg abstract in this paper the work initiated in part one and two is extended to the transient subgrid scale gradient subgrid scale sgs gsgs stabilized method temporal accuracy and stability of semi discrete and time discontinuous space time versions of the method are examined for transient advection diffusion reaction problems also for the above methods predictor multi corrector algorithms are analyzed with special emphasis on mass and source lumping which has been shown to enhance both stability and accuracy of explicit stabilized methods it will be shown that the parent supg sgs and sgs gsgs methods perform very similarly and that explicit predictor multi corrector mass source lumping practically retains the accuracy of the parent method while gaining stability

stabilization and shock capturing parameters in supg formulation of compressible flows abstract the streamline upwind petrov galerkin supg formulation is one of the most widely used stabilized methods in finite element computation of compressible flows it includes a stabilization parameter that is known as typically the supg formulation is used in combination with a shock capturing term that provides additional stability near the shock fronts the definition of the shock capturing term includes a shock capturing parameter in this paper we describe for the finite element formulation of compressible flows based on conservation variables new ways for determining the and the shock capturing parameter the new definitions for the shock capturing parameter are much simpler than the one based on the entropy variables involve less operations in calculating the shock capturing term and yield better shock quality in the test computations

unsteady free surface flow simulation over complex topography with a multidimensional upwind technique in the context of numerical techniques for solving unsteady free surface problems finite element and finite volume approximations are widely used a class of upwind methods which attempts to model the equations in a genuinely multidimensional manner has been recently introduced as an alternative multidimensional upwind schemes mus were developed initially for the approximation of steady state solutions of the two dimensional euler equations on unstructured grids although they can be applicable to any system of hyperbolic conservation laws such as the shallow water equations the formal analogy between the two systems of equations is useful for simple cases however in practical applications of interest in hydraulics complex geometries and bottom slope variation can lead to important numerical errors produced by an inadequate source term discretization this problem has been analyzed and in this work the necessity of a multidimensional upwind discretization of the source terms is justified the basis of the numerical method is stated and the particular adaptation to unsteady shallow water flows over irregular geometry is described as test cases laboratory experimental data are used together with academic tests for validation

a general framework to construct schemes satisfying additional conservation relations application to entropy conservative and entropy dissipative schemes abstract we are interested in the approximation of a steady hyperbolic problem in some cases the solution can satisfy an additional conservation relation at least when it is smooth this is the case of an entropy in this paper we show starting from the discretization of the original pde how to construct a scheme that is consistent with the original pde and the additional conservation relation since one interesting example is given by the systems endowed by an entropy we provide one explicit solution and show that the accuracy of the new scheme is at most degraded by one order in the case of a discontinuous galerkin scheme and a residual distribution scheme we show how not to degrade the accuracy this improves the recent results obtained in 1 2 3 4 in the sense that no particular constraints are set on quadrature formula and that a priori maximum accuracy can still be achieved we study the behavior of the method on a non linear scalar problem however the method is not restricted to scalar problems

skew selfadjoint form for systems of conservation laws abstract hyperbolic systems of conservation laws augumented with an entropy inequality are studied it is shown that such systems can be written in a quasilinear skew selfadjoint form centered differencing of such a form under the smooth regime ends up with a systematic recipe for constructing quasiconservative schemes where the global entropy conservation is recovered employing the above formulation in bounded regions under the nonsmooth regime as well a local entropy decay estimate is also concluded examples of the shallow water and the full gasdynamics equations are explicitly treated

well balanced residual distribution for the ale spherical shallow water equations on moving adaptive meshes we consider the numerical approximation of the shallow water equations swes in spherical geometry for oceanographic applications to provide enhanced resolution of moving fronts present in the flow we consider adaptive discrete approximations on moving triangulations of the sphere to this end we restate all arbitrary lagrangian eulerian ale transport formulas as well as the volume transformation laws for a 2d manifold using these results we write the set of ale swes on the sphere we then propose a residual distribution discrete approximation of the governing equations classical properties as the dgcl and the c property well balancedness are reformulated in this more general context an adaptive mesh movement strategy is proposed the discrete framework obtained is thoroughly tested on standard benchmarks in large scale oceanography to prove their potential as well as the advantage brought by the adaptive mesh movement

energy stable staggered schemes for the shallow water equations abstract we focus on the development and analysis of staggered schemes for the two dimensional non linear shallow water equations with varying bathymetry semi implicit and fully explicit time discretizations are proposed particular attention is paid on non linear stability results principally considered here through discrete energy dissipation arguments to address such an issue specific convective fluxes are employed implying diffusive terms relying on the pressure gradient in addition of providing an explicit control of the discrete energy budget the method is shown to preserve motionless steady states as well as the positivity of the water height these properties are still satisfied in a fully explicit context provided an appropriate discretization of the pressure gradient these stability results make the approach particularly robust and efficient for both coastal flows and low froude number regimes as a result in addition of a great ease of implementation the presented schemes meet the operational requirements attached to the simulation of large and small scale oceanic flows

an efficient dynamically adaptive mesh for potentially singular solutions abstract we develop an efficient dynamically adaptive mesh generator for time dependent problems in two or more dimensions the mesh generator is motivated by the variational approach and is based on solving a new set of nonlinear elliptic pdes for the mesh map when coupled to a physical problem the mesh map evolves with the underlying solution and maintains high adaptivity as the solution develops complicated structures and even singular behavior the overall mesh strategy is simple to implement avoids interpolation and can be easily incorporated into a broad range of applications the efficacy of the mesh is first demonstrated by two examples of blowing up solutions to the 2 d semilinear heat equation these examples show that the mesh can follow with high adaptivity a finite time singularity process the focus of applications presented here is however the baroclinic generation of vorticity in a strongly layered 2 d boussinesq fluid a challenging problem the moving mesh follows effectively the flow resolving both its global features and the almost singular shear layers developed dynamically the numerical results show the fast collapse to small scales and an exponential vorticity growth

the ivp for the benjamin ono equation in weighted sobolev spaces abstract in this work we continue our study initiated in fonseca and ponce 2011 11 on the uniqueness properties of real solutions to the ivp associated to the benjamin ono bo equation in particular we shall show that the uniqueness results established in fonseca and ponce 2011 11 do not extend to any pair of non vanishing solutions of the bo equation also we shall prove that the uniqueness result established in fonseca and ponce 2011 11 under a hypothesis involving information of the solution at three different times cannot be relaxed to two different times

finite element methods for first order hyperbolic systems with particular emphasis on the compressible euler equations a petrov galerkin finite element formulation is presented for first order hyperbolic systems of conservation laws with particular emphasis on the compressible euler equations applications of the methodology are made to one and two dimensional steady and unsteady flows with shocks results obtained suggest the potential of the type of methods developed

well posedness for the two dimensional generalized zakharov kuznetsov equation in anisotropic weighted sobolev spaces abstract we consider the well posedness of the initial value problem associated to the k generalized zakharov kuznetsov equation in fractional weighted sobolev spaces h s r 2 l 2 x 2 r 1 y 2 r 2 d x d y s r 1 r 2 r our method of proof is based on the contraction mapping principle and it mainly relies on the well posedness results recently obtained for this equation in the sobolev spaces h s r 2 and a new pointwise commutator type formula involving the group induced by the linear part of the equation and the fractional anisotropic weights to be considered

computing average shaped tissue probability templates this note presents a framework for generating tissue probability maps that represent the average shape of a number of subjects brain images the procedure is formulated as finding maximum a posteriori estimates within a probabilistic generative model estimating the parameters involves alternating between estimating the deformations that match tissue class images of individual subjects to template and updating the template according to the latest estimates of the deformations a multinomial matching criterion is used such that multiple tissue class images e g grey and white matter are registered simultaneously with the current template estimate in order to generalise the resulting template to a broader range of subjects a template blurriness prior is included within the model

high order residual distribution scheme for the time dependent euler equations of fluid dynamics abstract in the present work a high order finite element type residual distribution scheme is designed in the framework of multidimensional compressible euler equations of gas dynamics the strengths of the proposed approximation rely on the generic spatial discretization of the model equations using a continuous finite element type approximation technique while avoiding the solution of a large linear system with a sparse mass matrix which would come along with any standard ode solver in a classical finite element approach to advance the solution in time in this work we propose a new residual distribution rd scheme which provides an arbitrary explicit high order approximation of the smooth solutions of the euler equations both in space and time the design of the scheme via the coupling of the rd formulation ricchiuto and abgrall 2010 abgrall 2006 with a deferred correction dec type method liu et al 2008 minion 2003 allows to have the matrix associated to the update in time which needs to be inverted to be diagonal the use of bernstein polynomials as shape functions guarantees that this diagonal matrix is invertible and ensures strict positivity of the resulting diagonal matrix coefficients this work is the extension of abgrall et al 2016 and abgrall 2017 to multidimensional systems we have assessed our method on several challenging benchmark problems for one and two dimensional euler equations and the scheme has proven to be robust and to achieve the theoretically predicted high order of accuracy on smooth solutions

on well posedness for the benjamin ono equation we prove existence and uniqueness of solutions for the benjamin ono equation with data in h s mathbb r s 1 4 moreover the flow is holder continuous in weaker topologies