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On the stability of totally upwind schemes for the hyperbolic initial boundary value problem

Abstract : In this paper, we present a numerical strategy to check the strong stability (or GKS-stability) of one-step explicit totally upwind scheme in 1D with numerical boundary conditions. The underlying approximated continuous problem is a hyperbolic partial differential equation. Our approach is based on the Uniform Kreiss-Lopatinskii Condition, using linear algebra and complex analysis to count the number of zeros of the associated determinant. The study is illustrated with the Beam-Warming scheme together with the simplified inverse Lax-Wendroff procedure at the boundary.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03732720
Contributor : Benjamin Boutin Connect in order to contact the contributor
Submitted on : Thursday, July 21, 2022 - 10:30:30 AM
Last modification on : Monday, July 25, 2022 - 11:01:46 AM

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Distributed under a Creative Commons Attribution - ShareAlike 4.0 International License

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  • HAL Id : hal-03732720, version 1
  • ARXIV : 2207.10978

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Benjamin Boutin, Pierre Le Barbenchon, Nicolas Seguin. On the stability of totally upwind schemes for the hyperbolic initial boundary value problem. 2022. ⟨hal-03732720⟩

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