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On an Essentially Conservative Scheme for Hyperbolic Conservation Laws
Journal of Computational Physics, 1994This paper is concerned with the numerical solution of scalar equations and systems of conservation laws. In the first part of the paper the author proposes an essentially conservative second-order scheme, proving that it satisfies the so called total variation bounded (TVB) property.
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Conservation laws and their hyperbolic regularizations
Journal of Mathematical Sciences, 2010The authors study hyperbolic regularizations of conservation laws. Multi-dimensional linear conservation laws contain conservative and non-equilibrium variables. The Chapman-Enskog conjecture states that non-equilibrium variables can be expressed via the conservative ones, closing the problem. The authors consider this conjecture in the linear case for
Palin, V. V., Radkevich, E. V.
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A composite semi-conservative scheme for hyperbolic conservation laws
Applied Mathematics and Computation, 2010The author uses a non-conservative form of conservation laws to construct a semi-conservative scheme which becomes conservative in the neighborhood of a discontinuity. The proposed scheme captures the shock with high accuracy but yields rarefaction shocks in the presence of a sonic point.
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Hyperbolic Conservation Laws and L2
2018Taking as background the fact that conservation laws in a single space variable are well-posed in the space of functions of bounded variation, while multidimensional systems enjoy short-time well-posedness in Sobolev spaces Hs, we attempt to resolve the discrepancies between these two theories by exploring what can be said about stability of one ...
Barbara Lee Keyfitz, Hao Ying
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On conservation laws for hyperbolized equations
Differential Equations, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Surnachev, M. D. +2 more
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Hyperbolic regularizations of conservation laws
Russian Journal of Mathematical Physics, 2008The investigations of problems in kinetics for hyperbolic regularizations of conservation laws, initiated by Volevich and Radkevich, regarding the Chapman-Enskog conjecture are continued in the work. The objective is to carry out the study of the conjecture in the linear case for linearized problems.
Palin, V. V., Radkevich, E. V.
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Primitive, Conservative and Adaptive Schemes for Hyperbolic Conservation Laws
1998For the last two or three decades, it has become an accepted practice to utilise conservative methods when solving numerically hyperbolic conservation laws. Shock waves are the solution features that demand the utilisation of conservative methods. Practical computational experience shows that the use of a non-conservative method results in the wrong ...
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