material state remapping in computational solid mechanics a computational procedure for remapping material state information from one finite element mesh to another is described the procedure is useful in connection with evolving meshes for inelastic problems as for example occur in the context of fracture simulation and adaptive mesh refinement the proposed method is based on weak enforcement of equality between corresponding fields on the two meshes where piecewise constant fields on both meshes are generalized from the quadrature point values the essential algorithmic problem is that of calculating the volume partition of an arbitrary convex region with respect to a covering set of disjoint convex regions instead of geometrically resolving the associated intersections the problem is herein approximated by a constrained optimization problem which may be readily and efficiently solved computationally this formulation is a main contribution of the paper computational examples are given that illustrate the effectiveness of the proposed procedure copyright 2002 john wiley sons ltd

optimization based remap and transport a divide and conquer strategy for feature preserving discretizations this paper examines the application of optimization and control ideas to the formulation of feature preserving numerical methods with particular emphasis on the conservative and bound preserving remap constrained interpolation and transport advection of a single scalar quantity we present a general optimization framework for the preservation of physical properties and specialize it to a generic optimization based remap obr of mass density the latter casts remap as a quadratic program whose optimal solution minimizes the distance to a suitable target quantity subject to a system of linear inequality constraints the approximation of an exact mass update operator defines the target quantity which provides the best possible accuracy of the new masses without regard to any physical constraints such as conservation of mass or local bounds the latter are enforced by the system of linear inequalities in so doing the generic obr formulation separates accuracy considerations from the enforcement of physical properties we proceed to show how the generic obr formulation yields the recently introduced flux variable flux target fvft 1 and mass variable mass target mvmt 2 formulations of remap and then follow with a formal examination of their relationship using an intermediate flux variable mass target fvmt formulation we show the equivalence of fvft and mvmt optimal solutions to underscore the scope and the versatility of the generic obr formulation we introduce the notion of adaptable targets i e target quantities that reflect local solution properties extend fvft and mvmt to remap on the sphere and use obr to formulate adaptable conservative and bound preserving optimization based transport algorithms for cartesian and latitude longitude coordinate systems a selection of representative numerical examples on two dimensional grids demonstrates the computational properties of our approach

conformal deformation to constant negative scalar curvature on noncompact riemannian manifolds si m g est une variete de riemann complete de courbure scalaire non positive s satisfaisant s x e 0 pour x m m 0 ou m 0 est un ensemble compact alors il y a une metrique conforme complete g de courbure scalaire s 1

a synchronous and iterative flux correction formalism for coupled transport equations many problems of fluid dynamics involve the coupled transport of several density like dependent variables for instance densities of mass and momenta in elastic flows in this paper a conservative and synchronous flux corrected transport fct formalism is developed which aims at a consistent transport of such variables the technique differs from traditional fct algorithms in two respects first the limiting of transportive fluxes of the primary variables e g mass and momentum does not derive from smooth estimates of the variables but it derives from analytic constraints implied by the lagrangian form of the governing continuity equations which are imposed on the specific mixing ratios of the variables e g velocity components second the traditional fct limiting based on sufficiency conditions is augmented by an iterative procedure which approaches the necessity requirements this procedure can also be used in the framework of traditional fct schemes and a demonstration is provided that it can significantly reduce some of the pathological behaviors of fct algorithms although the approach derived is applicable to the transport of arbitrary conserved quantities it is particularly useful for the synchronous transport of mass and momenta in elastic flows where it assures intrinsic stability of the algorithm regardless of the magnitude of the mass density variable this latter property becomes especially important in fluids with large density variations or in models with a material vertical coordinate e g geophysical hydrostatic stratified flows in isopycnic isentropic coordinates where material surfaces can collapse to zero mass layers admitting therefore arbitrarily large local courant numbers

compatible fluxes for van leer advection application of the standard second order upstream centered advection method of van leer to a coupled transport equation system of the form t a a u 0 can produce artificial extrema in the ratiot a even thoughtsatisfies a simple advection equation and is expected to preserve monotonicity hereuis velocity is mass density andais a conserved quantity such as momentum density energy density or chemical species density thustis a mass specific transport quantity such as velocity energy per unit mass temperature or species mass fraction a new flux formulation and gradient limiting procedure is presented here which eliminates these artificial extrema preserves the second order accuracy and preserves the monotone character of the van leer method even in the limit of vanishing mass density such a formulation is calledcompatible the method is noniterative i e explicit and can be employed in a general finite volume framework sample results for the transport of a square wave in one and two dimensions are provided

isometry invariant solutions to a critical problem on non compact riemannian manifolds abstract we analyse an elliptic equation with critical growth set on a d dimensional d 3 hadamard manifold m g by adopting a variational perspective we prove the existence of non zero non negative solutions invariant under the action of a specific family of isometries our result remains valid when the original nonlinearity is singularly perturbed preserving the same variational approach but considering other groups of isometries we finally show that when m r d d 3 and the nonlinearity is odd there exist at least 1 d d 3 2 pairs of sign changing solutions

implementation of the jacobian free newton krylov method for solving the first order ice sheet momentum balance we have implemented the jacobian free newton krylov jfnk method for solving the first order ice sheet momentum equation in order to improve the numerical performance of the glimmer community ice sheet model glimmer cism the land ice component of the community earth system model cesm our jfnk implementation is based on significant re use of existing code for example our physics based preconditioner uses the original picard linear solver in glimmer cism for several test cases spanning a range of geometries and boundary conditions our jfnk implementation is 1 8 3 6 times more efficient than the standard picard solver in glimmer cism importantly this computational gain of jfnk over the picard solver increases when refining the grid global convergence of the jfnk solver has been significantly improved by rescaling the equation for the basal boundary condition and through the use of an inexact newton method while a diverse set of test cases show that our jfnk implementation is usually robust for some problems it may fail to converge with increasing resolution as does the picard solver globalization through parameter continuation did not remedy this problem and future work to improve robustness will explore a combination of picard and jfnk and the use of homotopy methods

a conservative semi lagrangian multi tracer transport scheme cslam on the cubed sphere grid a conservative multi tracer transport algorithm on the cubed sphere based on the semi lagrangian approach cslam has been developed the scheme relies on backward trajectories and the resulting upstream cells polygons are approximated with great circle arcs biquadratic polynomial functions are used for approximating the density distribution in the cubed sphere grid cells the upstream surface integrals associated with the conservative semi lagrangian scheme are computed as line integrals by employing the gauss green theorem the line integrals are evaluated using a combination of exact integrals and high order gaussian quadrature the upstream cell trajectories information and computation of weights of integrals can be reused for each additional tracer the cslam scheme is extensively tested with various standard benchmark test cases of solid body rotation and deformational flow in both cartesian and spherical geometry and the results are compared with those of other published schemes the cslam scheme is accurate robust and moreover the edges and vertices of the cubed sphere discontinuities do not affect the overall accuracy of the scheme the cslam scheme exhibits excellent convergence properties and has an option for enforcing monotonicity the advantages of introducing cross terms in the fully two dimensional biquadratic density distribution functions are also examined in the context of cartesian as well as the cubed sphere grid which has six local sub domains with discontinuous edges and corners

adaptive moment of fluid method a novel adaptive mesh refinement amr strategy based on the moment of fluid mof method for volume tracking of evolving interfaces is presented moment of fluid method is a new interface reconstruction and volume advection method using volume fractions as well as material centroids the mesh refinement criterion is based on the deviation of the actual centroid obtained by interface reconstruction from the reference centroid given by moment advection process the centroid error indicator detects not only high curvature regions but also regions with complicated subcell structures like filaments a new lagrange remap scheme is presented for advecting moments which includes lagrangian backtracking polygon intersection based remapping and forward tracking to define the material centroid the effectiveness and efficiency of amr mof method is demonstrated with classical test problems such as zalesak s disk and reversible vortex problem the comparison with previously published results for these problems shows the superior accuracy of the amr mof method over other methods in addition two new test cases with severe deformation rates are introduced namely droplet deformation and s shape deformation problems for further demonstration of the capabilities of the amr mof method

infinitely many nonradial solutions of a euclidean scalar field equation abstract we study the equation u b x u x u x r n u h 1 r n the existence of a nonradial solution has been an open problem for some time even in the autonomous case under suitable hypotheses mainly on we find an unbounded sequence of nonradial solutions if n 4 or n 6 we also obtain infinitely many solutions if b and are not rotationally symmetric with respect to x but satisfy only a weaker symmetry

combined effects of singular and superlinear nonlinearities in some singular boundary value problems abstract this paper deals with a class of singular semilinear elliptic dirichlet boundary value problems where the combined effects of a superlinear and a singular term allow us to establish some existence and multiplicity results

the repair paradigm new algorithms and applications to compressible flow the repair paradigm leads to several algorithms for redistributing mass momentum and energy while adhering to local maximum principles as an adjunct to the remapping step in certain compressible flow codes that use remapping such as arbitrary lagrangian eulerian codes or for just redistributing mass in advection codes in the case of advection of a concentration repair keeps the newly computed concentration in a cell between the maximum and minimum concentrations in neighboring old cells thus guaranteeing at least that the new concentration is between zero and one for compressible flow density velocity and internal energy are similarly constrained while maintaining conservation of mass momentum and total energy in this way positive density and internal energy are achieved as a side effect we propose a new algorithm combining both local and global repair that maintains causality and is efficient in a parallel computational setting the local global algorithm is independent of the order in which the distribution is performed and it maintains 1d symmetry this is applied to advection in two dimensions and to among others the leblanc problem the sedov problem and an interacting 2d blast wave problem the latter is done with a lagrangian code for which rezoning remapping and repair are essential

compatible energy conserving bounds preserving remap of hydrodynamic fields for an extended ale scheme abstract from the very origins of numerical hydrodynamics in the lagrangian work of von neumann and richtmyer 83 the issue of total energy conservation as well as entropy production has been problematic because of well known problems with mesh deformation lagrangian schemes have evolved into arbitrary lagrangian eulerian ale methods 39 that combine the best properties of lagrangian and eulerian methods energy issues have persisted for this class of methods we believe that fundamental issues of energy conservation and entropy production in ale require further examination the context of the paper is an ale scheme that is extended in the sense that it permits cyclic or periodic remap of data between grids of the same or differing connectivity the principal design goals for a remap method then consist of total energy conservation bounded internal energy and compatibility of kinetic energy and momentum we also have secondary objectives of limiting velocity and stress in a non directional manner keeping primitive variables monotone and providing a higher than second order reconstruction of remapped variables in particular the new contributions fall into three categories associated with energy conservation and entropy production reconstruction and bounds preservation of scalar and tensor fields and conservative remap of nonlinear fields the paper presents a derivation of the methods details of implementation and numerical results for a number of test problems the methods requires volume integration of polynomial functions in polytopal cells with planar facets and the requisite expressions are derived for arbitrary order

constrained interpolation remap of divergence free fields abstract a novel constrained interpolation algorithm for remapping of solenoidal face finite element vector fields is presented the algorithm is based on explicit recovery postprocessing and interpolation of a potential for the original vector field and a subsequent application of a curl operator to obtain the desired divergence free finite element field on the new mesh the use of interpolation instead of advection in the remap process offers valuable computational advantages old and new meshes are neither required to have the same connectivity nor to be close to each other slope limiting and upwinding which can be sensitive to grid structure are avoided and replaced by local optimization to control energy of the remapped field the new method is validated using a suite of cyclic remap problems on random and tensor product mesh sequences a comparison with a local remapper based on a constrained transport advection algorithm is also included

conservative multimoment transport along characteristics for discontinuous galerkin methods a set of algorithms based on characteristic discontinuous galerkin methods is presented for tracer transport on the sphere the algorithms are designed to reduce message passing interface communica

a multistep flux corrected transport scheme a multistep flux corrected transport mfct scheme is developed to achieve conservative and monotonic tracer transports for multistep dynamical cores mfct extends zalesak two time level scheme to any multistep time differencing schemes by including multiple high order fluxes in the antidiffusive flux while computing the two time level low order monotone solution the multistep time differencing scheme used in this study is the third order adams bashforth ab3 scheme implemented in a finite volume icosahedral shallow water model the accuracy of ab3 mfct is quantified by the shape preserving advection experiments in non divergent flow as well as a cosine bell whose shape changes during advection in shear flow ab3 mfct has been shown to be insensitive to time step size this make ab3 mfct an attractive transport scheme for explicit high resolution model applications with small time step mfct is tested in shallow water model simulations to demonstrate that the use of mfct maintains positive definite tracer transport while at the same time conserving both fluid mass and tracer mass within round off errors in the ab3 dynamic core

incremental remapping as a transport advection algorithm there are two fundamentally different strategies for solving the standard transport or continuity equation corresponding to whether it is expressed as a partial differential equation or as an integral statement of conservation the more common approach is to discretize the partial differential equation and to march the solution forward in time the alternative method is to project cell volumes along lagrangian trajectories as far forward or backward in time as desired and then to remap the resulting density distribution onto some target mesh this latter approach is known as remapping remapping has many advantages not the least of which is that the time step is limited only by accuracy considerations but it tends to be expensive and complex in this paper we show that if the time step is made sufficiently short such that trajectories are confined to the nearest neighbor cells then the remapping may be written as a flux form transport algorithm and it becomes nearly as simple and efficient as standard transport schemes the resulting method called incremental remapping retains most of the advantages of general remapping these include a geometric basis for transport b compatibility of associated tracer transport with simple tracer advection i e retention of tracer monotonicity properties and c efficient handling of multiple tracers since each additional tracer adds only a relatively small incremental cost

reprint of atmospheric models used for practical climate simulation must be capable handling the transport of hundreds of tracers for computational efficiency conservative multi tracer semi lagrangian type transport schemes are appropriate global models based on high order galerkin approach employ highly non uniform spectral element grids and semi lagrangian transport is a challenge on those grids a conservative semi lagrangian scheme spelt spectral element lagrangian transport employing a multi moment compact reconstruction procedure is developed for non uniform quadrilateral grids the scheme is based on a characteristic semi lagrangian method that avoids complex and expensive upstream area computations the spelt scheme has been implemented in the high order method modeling environment homme which is based on a cubed sphere grid with spectral element spatial discretization additionally we show the strong scalability and multi tracer efficiency using several benchmark tests the spelt solution can be made monotonic positivity preserving by combining the flux corrected transport algorithm which is demonstrated on a uniform resolution grid in particular spelt can be efficiently used for non uniform grids and provides accurate and stable results for high resolution meshes

positive solutions of yamabe type equations on complete manifolds and applications we study the semilinear equation u a x u b x u 1 on a complete riemannian manifold we determine conditions on the coefficients that guarantee existence and nonexistence of positive solutions a very general uniqueness result is also established our main results are valid without explicit curvature assumptions and appear to be new even in rm

optimization based mesh correction with volume and convexity constraints we consider the problem of finding a mesh such that 1 it is the closest with respect to a suitable metric to a given source mesh having the same connectivity and 2 the volumes of its cells match a set of prescribed positive values that are not necessarily equal to the cell volumes in the source mesh this volume correction problem arises in important simulation contexts such as satisfying a discrete geometric conservation law and solving transport equations by incremental remapping or similar semi lagrangian transport schemes in this paper we formulate volume correction as a constrained optimization problem in which the distance to the source mesh defines an optimization objective while the prescribed cell volumes mesh validity and or cell convexity specify the constraints we solve this problem numerically using a sequential quadratic programming sqp method whose performance scales with the mesh size to achieve scalable performance we develop a specialized multigrid based preconditioner for optimality systems that arise in the application of the sqp method to the volume correction problem numerical examples illustrate the importance of volume correction and showcase the accuracy robustness and scalability of our approach

tracer transport within an unstructured grid ocean model using characteristic discontinuous galerkin advection abstract in a previous article a characteristic discontinuous galerkin cdg advection scheme was presented for tracer transport lee et al 2016 the scheme is conservative unconditionally stable with respect to time step and scales sub linearly with the number of tracers being advected here we present the implementation of the cdg advection scheme for tracer transport within mpas ocean a boussinesque unstructured grid ocean model with an arbitrary lagrangian eulerian vertical coordinate the scheme is implemented in both the vertical and horizontal dimensions and special care is taken to ensure that the scheme remains conservative in the context of moving vertical layers consistency is ensured with respect to the dynamics by a renormalization of the fluxes with respect to the volume fluxes derived from the continuity equation for spherical implementations the intersection of the flux swept regions and the eulerian grid are determined for great circle arcs and the fluxes and element assembly are performed on the plane via a length preserving projection solutions are presented for a suite of test cases and comparisons made to the existing flux corrected transport scheme in mpas ocean

a forward trajectory global semi lagrangian transport scheme a forward trajectory semi lagrangian scheme for advection on the surface of the sphere is proposed the advection scheme utilizes the forward downstream trajectory originating at eulerian grid points and cascade interpolation a sequence of 1d interpolations to transfer data from the downstream lagrangian points to the eulerian points a new and more accurate algorithm determines pole values the resulting forward trajectory semi lagrangian scheme can easily incorporate high order trajectory integration methods this avoids the standard iterative process in a typical backward trajectory scheme two third order accurate schemes and a second order accurate scheme are presented a mass conservative version of the forward trajectory semi lagrangian scheme is also derived within the cascade interpolation framework mass from a lagrangian cell is transferred to the corresponding eulerian cell with two 1d remappings through an intermediate cell system mass in the polar region is redistributed by way of an efficient local approximation the resulting scheme is globally conservative but restricted to meridional courant number c 1

implementation of the jacobian free newton krylov method for solving the for solving the first order ice sheet momentum balance we have implemented the jacobian free newton krylov jfnk method for solving the rst order ice sheet momentum equation in order to improve the numerical performance of the community ice sheet model cism the land ice component of the community earth system model cesm our jfnk implementation is based on signicant re use of existing code for example our physics based preconditioner uses the original picard linear solver in cism for several test cases spanning a range of geometries and boundary conditions our jfnk implementation is 1 84 3 62 times more efficient than the standard picard solver in cism importantly this computational gain of jfnk over the picard solver increases when rening the grid global convergence of the jfnk solver has been signicantly improved by rescaling the equation for the basal boundary condition and through the use of an inexact newton method while a diverse set of test cases show that our jfnk implementation is usually robust for some problems it may fail to converge with increasing resolution as does the picard solver globalization through parameter continuation did not remedy this problem and future work to improve robustness will explore a combination of picard and jfnk and the use of homotopy methods

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

on simplifying incremental remap based transport schemes the flux form incremental remapping transport scheme introduced by dukowicz and baumgardner 1 converts the transport problem into a remapping problem this involves identifying overlap areas between quadrilateral flux areas and regular square grid cells which is non trivial and leads to some algorithm complexity in the simpler swept area approach originally introduced by hirt et al 2 the search for overlap areas is eliminated even if the flux areas overlap several regular grid cells the resulting simplified scheme leads to a much simpler and robust algorithm we show that for sufficiently small courant numbers approximately cfl 1 2 the simplified or swept area scheme can be more accurate than the original incremental remapping scheme this is demonstrated through a von neumann stability analysis an error analysis and in idealized transport test cases on the sphere using the incremental remapping based scheme called ff cslam flux form version of the conservative semi lagrangian multi tracer scheme on the cubed sphere

idr s a family of simple and fast algorithms for solving large nonsymmetric systems of linear equations we present idr s a new family of efficient short recurrence methods for large nonsymmetric systems of linear equations the new methods are based on the induced dimension reduction idr method proposed by sonneveld in 1980 idr s generates residuals that are forced to be in a sequence of nested subspaces although idr s behaves like an iterative method in exact arithmetic it computes the true solution using at most n n s matrix vector products with n the problem size and s the codimension of a fixed subspace we describe the algorithm and the underlying theory and present numerical experiments to illustrate the theoretical properties of the method and its performance for systems arising from different applications our experiments show that idr s is competitive with or superior to most bi cg based methods and outperforms bi cgstab when s 1

hybrid bi cg methods with a bi cg formulation closer to the idr approach the induced dimension reduction s idr s method has recently been developed sleijpen et al have reformulated the bi conjugate gradient stabilized bicgstab method to clarify the relationship between bicgstab and idr s the formulation of bi conjugate gradient bi cg part used in the reformulated bicgstab is different from that of the original bi cg method the bi cg coefficients are computed by a formulation that is closer to the idr approach in this paper we will redesign variants of the conjugate gradient squared method cgs method bicgstab and the generalized product type method derived from bi cg gpbicg bicg mr2 by using the bi cg formulation that is closer to the idr approach although our proposed variants are mathematically equivalent to their counterparts the computation of one of the bi cg coefficients differs and the recurrences of the variants are also partly different from those of the original hybrid bi cg methods numerical experiments show that the variants of bicgstab and gpbicg bicg mr2 are more stable and lead to faster convergence typically for linear systems for which the methods converge slowly long stagnation phase and that the variants of cgs attain more accurate approximate solutions

second order accurate volume tracking based on remapping for triangular meshes this paper presents a second order accurate piecewise linear volume tracking based on remapping for triangular meshes this approach avoids the complexity of extending unsplit second order volume of fluid algorithms advection methods on triangular meshes the method is based on lagrangian eulerian le methods therefore it does not deal with edge fluxes and corner fluxes flux corrections as is typical in advection algorithms the method is constructed of three parts a lagrangian phase a reconstruction phase and a remapping phase in the lagrangian phase the original eulerian grid is projected along trajectories to obtain lagrangian grids in practice this projection is handled through the time integration of velocity field for grid vertices at each time step the reconstruction is based on truncating the volume material polygon for each lagrangian mixed grid since in piecewise linear approximation the interface is represented by a segment line the polygon material truncation is mainly finding the segment interface finding the segment interface is calculating the line normal and line constant at each multi fluid cell details of applying two normal calculation methods differential and geometric least squares gls methods are given while the gls method exhibits second order accurate approximation in reproducing circular interfaces the differential least squares dls method results in a first order accurate representation of the interface the last part of the algorithm which is remapping of the volume materials from the lagrangian grid to the original one is performed by a series of polygon intersection procedures the behavior of the algorithm is investigated for flow fields with constant interface topology and flow fields inducing large interfacial stretching and tearing second order accuracy is obtained if the velocity integration as well as the reconstruction steps are at least second order accurate

the repair paradigm and application to conservation laws repair is a conservative post processing procedure to be used in numerical methods for hyperbolic conservation laws in order to preserve certain qualitative characteristics of the numerical solution such as positivity of density and internal energy by means of redistribution of conserved quantities such as mass momentum and total energy among the cells of the mesh in this paper we describe the repair paradigm and prove several theorems which form a theoretical foundation for the repair procedures we consider two applications of repair and present corresponding numerical results the first application deals with improving properties of the remapping conservative interpolation stage of arbitrary lagrangian eulerian ale methods for the gas dynamics equations in which the solution is conservatively transferred from one mesh to another one requirement for remapping is that the interpolated density and internal energy on the new mesh have to stay positive another desirable property is that the remapping procedure should not create new extrema for the velocity field for various reasons these properties may not be satisfied especially for high order methods repair plays a supplemental role by bringing gas dynamics quantities into physically justified bounds another application of repair is to improve the quality of numerical methods for advection of some scalar tracer field with prescribed divergence free velocity field in which case the advection equation can be written as a conservation law and therefore the total amount of tracer is conserved we show how the repair procedure allows us to reduce oscillations in a numerical solution obtained by a formally high order method repair offers an alternative to more classical methods of reducing oscillations and maintaining positivity

a semi lagrangian discontinuous galerkin method for scalar advection by incompressible flows a new conservative semi lagrangian formulation is proposed for the discretization of the scalar advection equation in flux form the approach combines the accuracy and conservation properties of the discontinuous galerkin dg method with the computational efficiency and robustness of semi lagrangian sl techniques unconditional stability in the von neumann sense is proved for the proposed discretization in the one dimensional case a monotonization technique is then introduced based on the flux corrected transport approach this yields a multi dimensional monotonic scheme for the piecewise constant component of the computed solution that is characterized by a smaller amount of numerical diffusion than standard dg methods the accuracy and stability of the method are further demonstrated by two dimensional tracer advection tests in the case of incompressible flows the comparison with results obtained by standard sl and dg methods highlights several advantages of the new technique

second invariant preserving remap of the 2d deviatoric stress tensor in ale methods abstract for numerical simulations of impact problems or fluid solid interactions the ale arbitrary lagrangian eulerian approach is a useful tool due to its ability to keep the computational mesh smooth and moving with the fluid the elastic plastic extension of the compressible fluid model requires tensor variables for the description of non volumetric deviatoric mechanical stress while lagrangian numerical schemes based on the evolution equation of the stress tensor are well developed tensor remap is still a relatively unexplored territory we propose a new approach to deviatoric stress remapping where the second invariant j 2 a conservative scalar quantity related to the strain energy is remapped independently of the tensor components these are re scaled to match the remapped invariant value effectively using only the principal directions and eigenvalue ratio from the component wise remap this approach is frame invariant preserves j 2 invariant bounds and conserves the total invariant we compare our method with component based remapping using a simple synchronized limiter or a specialized stress tensor limiter described in the literature

a second order accurate material order independent interface reconstruction technique for multi material flow simulations a new second order accurate volume conservative material order independent interface reconstruction method for multi material flow simulations is presented first materials are located in multi material computational cells using a piecewise linear reconstruction of the volume fraction function these material locator points are then used as generators to reconstruct the interface with a weighted voronoi diagram that matches the volume fractions the interfaces are then improved by minimizing an objective function that smoothes interface normals while enforcing convexity and volume constraints for the pure material subcells convergence tests are shown demonstrating second order accuracy static and dynamic examples are shown illustrating the superior performance of the method over existing material order dependent methods

a lax wendroff type theorem for unstructured quasi uniform grids a well known theorem of lax and wendroff states that if the sequence of approximate solutions to a system of hyperbolic conservation laws generated by a conservative consistent numerical scheme converges boundedly a e as the mesh parameter goes to zero then the limit is a weak solution of the system moreover if the scheme satisfies a discrete entropy inequality as well the limit is an entropy solution the original theorem applies to uniform cartesian grids this article presents a generalization for quasi uniform grids with lipschitz boundary cells uniformly continuous inhomogeneous numerical fluxes and nonlinear inhomogeneous sources the added generality allows a discussion of novel applications like local time stepping grids with moving vertices and conservative remapping a counterexample demonstrates that the theorem is not valid for arbitrary non quasi uniform grids

a class of deformational flow test cases for linear transport problems on the sphere a class of new benchmark deformational flow test cases for the two dimensional horizontal linear transport problems on the sphere is proposed the scalar field follows complex trajectories and undergoes severe deformation during the simulation however the flow reverses its course at half time and the scalar field returns to its initial position and shape this process makes the exact solution available at the end of the simulation and facilitates assessment of the accuracy of the underlying transport scheme a procedure to eliminate possible cancellations of errors when the flow reverses is proposed the test suite consists of four cases three are based on non divergent flow fields and one on a divergent flow the initial conditions are prescribed in terms of regular latitude longitude spherical coordinates and are easy to implement the divergent flow is specifically aimed for conservative global transport schemes to test for conservation consistency and monotonicity or positivity of limiters filters in a challenging flow environment in the context of semi lagrangian schemes the time varying flow fields can be used to test trajectory algorithms where the exact trajectories do not follow great circle arcs the characteristics of the test cases are demonstrated with two different transport schemes

regularity for multi phase variational problems abstract we prove c 1 regularity for local minimizers of the multi phase energy w d w p a x d w q b x d w s d x under sharp assumptions relating the couples p q and p s to the holder exponents of the modulating coefficients a and b respectively

a conservative multi tracer transport scheme for spectral element spherical grids atmospheric models used for practical climate simulation must be capable handling the transport of hundreds of tracers for computational efficiency conservative multi tracer semi lagrangian type transport schemes are appropriate global models based on high order galerkin approach employ highly non uniform spectral element grids and semi lagrangian transport is a challenge on those grids a conservative semi lagrangian scheme spelt spectral element lagrangian transport employing a multi moment compact reconstruction procedure is developed for non uniform quadrilateral grids the scheme is based on a characteristic semi lagrangian method that avoids complex and expensive upstream area computations the spelt scheme has been implemented in the high order method modeling environment homme which is based on a cubed sphere grid with spectral element spatial discretization additionally we show the strong scalability and multi tracer efficiency using several benchmark tests the spelt solution can be made monotonic positivity preserving by combining the flux corrected transport algorithm which is demonstrated on a uniform resolution grid in particular spelt can be efficiently used for non uniform grids and provides accurate and stable results for high resolution meshes