2016
DOI: 10.1016/j.amc.2015.04.085
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Abstract: a b s t r a c tWe study the conservative structure of linear Friedrichs systems with linear relaxation in view of the definition of well-balanced schemes. We introduce a particular global change of basis and show that the change-of-basis matrix can be used to develop a systematic treatment of well-balanced schemes in one dimension. This algebra sheds new light on a family of schemes proposed recently by Gosse (2011). The application to the S n model (a paradigm for the approximation of kinetic equations) for r… Show more

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Cited by 13 publications
(17 citation statements)
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“…Numerical simulation of VPFP systems was studied by several authors, see e.g. [16,33,38,42,11]. However, up to our knowledge, the numerical resolution of the high field limit has still not been studied and in particular no numerical comparisons with solutions of (2.5) are available.…”
Section: 1mentioning
confidence: 99%
“…Numerical simulation of VPFP systems was studied by several authors, see e.g. [16,33,38,42,11]. However, up to our knowledge, the numerical resolution of the high field limit has still not been studied and in particular no numerical comparisons with solutions of (2.5) are available.…”
Section: 1mentioning
confidence: 99%
“…First we consider the case λ = √ σ t µ/c, the case λ = − √ σ t µ/c will be discuss later. The second equation in (13) gives χ = − µ/σ t A T w ∈ R mo . One concludes that the one dimensional function…”
Section: Exponential Solutionsmentioning
confidence: 99%
“…When the scaling parameter ε → 0, the model problem admits a diffusion limit [22,8]. General references which provide accurate numerical methods for the diffusion limit are [3,8,19,27] for asymptotic-preserving methods and [13,20,21,26] for well-balanced methods. In principle, Trefftz method may be very efficient in the diffusion limit since the exact solutions in the cell have a perfect balance between the transport terms (matrices A 1 and A 2 ) and the relaxation (matrix R).…”
Section: Introductionmentioning
confidence: 99%
“…Under suitable conditions on the numerical flux F and under a stability condition of type σ(U n,− i+1/2 , U n,+ i+1/2 )∆t ≤ ∆x the fully discrete scheme (35) with the reconstruction at interfaces given by (32)- (33) Now, let us detail the scheme proposed by Berthon, Crestetto and Foucher in [12], based on an approximated Riemann solver strategy. They construct a well-balanced scheme based on Riemann approximate solver for the quasi-linear system (6) for a non-linear pressure with γ = 2.…”
Section: Propertiesmentioning
confidence: 99%
“…The 2D and 3D cases are relevant settings for real models for biology, but the step from 1D well-balanced schemes to 2D well-balanced schemes is stiff. Some first definitions of Godunov schemes in the 2D case have been proposed in [35,54] and are likely to produce new ideas to derive 2D well-balanced and asymptotic-preserving schemes.…”
Section: Propertiesmentioning
confidence: 99%