Entropy stability and the no-slip wall boundary condition

Magnus Svärd; Mark H. Carpenter; Matteo Parsani

doi:10.1137/16M1097225

Entropy stability and the no-slip wall boundary condition

Magnus Svärd, Mark H. Carpenter, Matteo Parsani

Applied Mathematics and Computational Science

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We present an entropy stable numerical scheme subject to no-slip wall boundary conditions. To enforce entropy stability only the no-penetration boundary condition and a temperature condition are needed at a wall, and this leads to an L² bound on the conservative variables. In this article, we take the next step and design a finite difference scheme that also bounds the velocity gradients. This necessitates the use of the full no-slip conditions.

Original language	English (US)
Pages (from-to)	256-273
Number of pages	18
Journal	SIAM Journal on Numerical Analysis
Volume	56
Issue number	1
DOIs	https://doi.org/10.1137/16M1097225
State	Published - 2018

Bibliographical note

Publisher Copyright:
© 2018 Society for Industrial and Applied Mathematics.

Keywords

Finite difference
Navier–Stokes
Nonlinear stability
Wall boundary conditions

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics
Numerical Analysis

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10.1137/16M1097225

Cite this

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AB - We present an entropy stable numerical scheme subject to no-slip wall boundary conditions. To enforce entropy stability only the no-penetration boundary condition and a temperature condition are needed at a wall, and this leads to an L2 bound on the conservative variables. In this article, we take the next step and design a finite difference scheme that also bounds the velocity gradients. This necessitates the use of the full no-slip conditions.

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KW - Navier–Stokes

KW - Nonlinear stability

KW - Wall boundary conditions

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Entropy stability and the no-slip wall boundary condition

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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