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Revisting High-Resolution Schemes with van Albada Slope Limiter

Communications on Applied Mathematics and Computation 2024年第3期6卷 1924-1953页

作者： Jingcheng Lu eitan tadmor Department of Mathematics University of MarylandCollege ParkMDUSA School of Mathematics University of MinnesotaMinneapolisMNUSA Department of Mathematics and Institute for Physical Sciences and Technology University ofMarylandCollegeParkMDUSA

Slope limiters play an essential role in maintaining the non-oscillatory behavior of high-resolution methods for nonlinear conservation *** family of minmod limiters serves as the prototype ***,we revisit the question of non-oscillatory behavior of high-resolution central schemes in terms of the slope limiter proposed by van Albada et al.(Astron Astrophys 108:76–84,1982).The van Albada(vA)limiter is smoother near extrema,and consequently,in many cases,it outperforms the results obtained using the standard minmod *** particular,we prove that the vA limiter ensures the one-dimensional Total-Variation Diminishing(TVD)stability and demonstrate that it yields noticeable improvement in computation of one-and two-dimensional systems.

关键词： High resolution Limiters Total-Variation Diminishing(TVD)stability Central schemes

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Constraint Preserving Schemes Using Potential-Based Fluxes *** Transport Equations

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Communications in Computational Physics 2011年第3期9卷 688-710页

作者： Siddhartha Mishra eitan tadmor Centre of Mathematics for Applications(CMA) University of OsloP.O.Box 1053BlindernN-0316 OsloNorway Center of Scientific Computation and Mathematical Modeling(CSCAMM) and Department of Mathematicsand Institute for Physical Sciences and Technology(IPST)University of MarylandMD 20742-4015USA

We consider constraint preserving multidimensional evolution equations.A prototypical example is provided by the magnetic induction equation of plasma *** constraint of interest is the divergence of the magnetic *** design finite volume schemes which approximate these equations in a stable manner and preserve a discrete version of the *** schemes are based on reformulating standard edge centered finite volume fluxes in terms of vertex centered *** potential-based approach provides a general framework for faithful discretizations of constraint transport and we apply it to both divergence preserving as well as curl preserving *** present benchmark numerical tests which confirm that our potential-based schemes achieve high resolution,while being constraint preserving.

关键词： Multidimensional evolution equations magnetohydrodynamics finite-difference finite volume schemes constraint transport potential-based schemes

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Non-Oscillatory Hierarchical Reconstruction for Central and Finite Volume Schemes

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Communications in Computational Physics 2007年第5期2卷 933-963页

作者： Yingjie Liu Chi-Wang Shu eitan tadmor Mengping Zhang School of Mathematics Georgia Institute of TechnologyAtlantaGA 30332-0160USA. Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA Department of Mathematics Institute for Physical Science and Technologyand Center of Scientific Computation and Mathematical Modeling(CSCAMM)University of MarylandCollege ParkMD 20742USA Department of Mathematics University of Science and Technology of ChinaHefeiAnhui 230026China

This is the continuation of the paper”Central discontinuous Galerkin methods on overlapping cells with a non-oscillatory hierarchical reconstruction”by the same *** hierarchical reconstruction introduced therein is applied to central schemes on overlapping cells and to finite volume schemes on non-staggered *** takes a new finite volume approach for approximating non-smooth solutions.A critical step for high-order finite volume schemes is to reconstruct a non-oscillatory high degree polynomial approximation in each cell out of nearby cell *** the paper this procedure is accomplished in two steps:first to reconstruct a high degree polynomial in each cell by using e.g.,a central reconstruction,which is easy to do despite the fact that the reconstructed polynomial could be oscillatory;then to apply the hierarchical reconstruction to remove the spurious oscillations while maintaining the high *** numerical computations for systems of conservation laws are performed without characteristic *** particular,we demonstrate that this new approach can generate essentially non-oscillatory solutions even for 5th-order schemes without characteristic decomposition.

关键词： Central scheme discontinuous Galerkin method ENO scheme finite volume scheme MUSCL scheme TVD scheme.

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