Journal ArticleDOI
A simplified TVD finite difference sheme via artificial viscousity
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TLDR
In this article, the total variation diminishing (TVD) finite difference scheme was interpreted as a Lax-Wendroff scheme plus an upwind weighted artificial dissipation term, which can be added to existing MacCormack method codes.Abstract:
In this paper we show that the total variation diminishing (TVD) finite difference scheme which was analysed by Sweby [8] can be interpreted as a Lax—Wendroff scheme plus an upwind weighted artificial dissipation term. We then show that if we choose a particular flux limiter and remove the requirement for upwind weighting, we obtain an artificial dissipation term which is based on the theory of TVD schemes, which does not contain any problem dependent parameters and which can be added to existing MacCormack method codes. Finally, we conduct numerical experiments to examine the performance of this new method.read more
Citations
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Journal ArticleDOI
Computational methods in Lagrangian and Eulerian hydrocodes
TL;DR: The basic explicit finite element and finite difference methods that are currently used to solve transient, large deformation problems in solid mechanics are reviewed.
Journal ArticleDOI
Numerical Hydrodynamics in Special Relativity
José María Martí,Ewald Müller +1 more
TL;DR: This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD), and particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD.
Journal ArticleDOI
Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity
TL;DR: A comprehensive summary of astrophysical simulations in strong gravitational fields is presented, detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do) overlap throughout the discussion.
Journal ArticleDOI
Numerical Hydrodynamics in General Relativity
TL;DR: The present update provides additional information on numerical schemes, and extends the discussion of astrophysical simulations in general relativistic hydrodynamics, with special mention of conservative and hyperbolic formulations well- adapted to advanced numerical methods.
Journal ArticleDOI
WhiskyMHD: a new numerical code for general relativistic magnetohydrodynamics
TL;DR: In this article, a new numerical code was developed to solve the full set of general-relativistic magnetohydrodynamics equations in a dynamical and arbitrary spacetime with high-resolution shock-capturing techniques on domains with adaptive mesh refinements.
References
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High resolution schemes for hyperbolic conservation laws
TL;DR: In this article, a class of new explicit second order accurate finite difference schemes for the computation of weak solutions of hyperbolic conservation laws is presented, which are obtained by applying a nonoscillatory first order accurate scheme to an appropriately modified flux function.
Journal ArticleDOI
High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws
TL;DR: The technique of obtaining high resolution, second order, oscillation free (TVD), explicit scalar difference schemes, by the addition of a limited antidiffusive flux to a first order scheme is described in this article.
Journal ArticleDOI
Upwind Second-Order Difference Schemes and Applications in Aerodynamic Flows
TL;DR: In this article, the authors consider the application of explicit Isecond-order, one-sided or "upwind," difference schemes for the numerical solution of hyperbolic systems in conservation-law form.
Proceedings ArticleDOI
High resolution applications of the Osher upwind scheme for the Euler equations
S. R. Chakravarthy,S. Osher +1 more
TL;DR: In this article, an upwind finite-difference method for hyperbolic systems of conservation laws, including the Euler equations, is presented for high resolution extension of the Osher scheme to second-order accuracy.