Journal ArticleDOI
Triangle based adaptive stencils for the solution of hyperbolic conservation laws
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TLDR
In this paper, a triangle-based total variation diminishing (TVD) scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedures.About:
This article is published in Journal of Computational Physics.The article was published on 1992-01-01. It has received 140 citations till now. The article focuses on the topics: Total variation diminishing & Hyperbolic partial differential equation.read more
Citations
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A high-order-accurate unstructured mesh finite-volume scheme for the advection-diffusion equation
TL;DR: This paper presents and analyze a new approach for high-order-accurate finite-volume discretization for diffusive fluxes that is based on the gradients computed during solution reconstruction, and introduces a technique for constraining the least-squares reconstruction in boundary control volumes.
Journal ArticleDOI
Divergence Correction Techniques for Maxwell Solvers Based on a Hyperbolic Model
TL;DR: A new method for incorporating Gauss' law into non-stationary electromagnetic simulation codes is developed, starting from a constrained formulation of the Maxwell equations and the resulting system is hyperbolic, and the divergence errors propagate with the speed of light to the boundary of the computational domain.
Journal ArticleDOI
High-order methods for the Euler and Navier–Stokes equations on unstructured grids
TL;DR: This article reviews several unstructured grid-based high-order methods for the compressible Euler and Navier–Stokes equations, and presents the basic design principles of each method, and highlights its pros and cons when appropriate.
Journal ArticleDOI
A monotone finite element scheme for convection-diffusion equations
Jinchao Xu,Ludmil T. Zikatanov +1 more
TL;DR: A simple technique is given in this paper for the construction and analysis of a class of finite element discretizations for convection-diffusion problems in any spatial dimension by properly averaging the PDE coefficients on element edges.
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Fully adaptive multiresolution finite volume schemes for conservation laws
TL;DR: The present paper is concerned with the development and the numerical analysis of fully adaptive multiresolution schemes, in which the solution is represented and computed in a dynamically evolved adaptive grid.
References
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Journal ArticleDOI
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Chi-Wang Shu,Stanley Osher +1 more
TL;DR: Two methods of sharpening contact discontinuities-the subcell resolution idea of Harten and the artificial compression idea of Yang, which those authors originally used in the cell average framework-are applied to the current ENO schemes using numerical fluxes and TVD Runge-Kutta time discretizations.
Journal ArticleDOI
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
ShuChi-Wang,OsherStanley +1 more
TL;DR: This work extends earlier work on the efficient implementation of ENO (essentially non-oscillatory) shock-capturing schemes by providing a new simplified expression for the ENO constructio...
Journal ArticleDOI
Uniformly high order accurate essentially non-oscillatory schemes, 111
TL;DR: An hierarchy of uniformly high-order accurate schemes is presented which generalizes Godunov's scheme and its second- order accurate MUSCL extension to an arbitrary order of accuracy.
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
Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme
TL;DR: Fromm's second-order scheme for integrating the linear convection equation is made monotonic through the inclusion of nonlinear feedback terms in this paper, where care is taken to keep the scheme in conservation form.
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