Bibliographic Details
| Title: |
A semi-implicit finite volume scheme for dissipative measure-valued solutions to the barotropic Euler system. |
| Authors: |
Arun, Koottungal Revi1 amoghk0720@iisertvm.ac.in, Krishnamurthy, Amogh1 amoghk0720@iisertvm.ac.in |
| Source: |
ESAIM: Mathematical Modelling & Numerical Analysis (ESAIM: M2AN). Jan/Feb2024, Vol. 58 Issue 1, p47-77. 31p. |
| Subject Terms: |
*FINITE volume method, *EULER equations, *ENTROPY |
| Abstract: |
A semi-implicit in time, entropy stable finite volume scheme for the compressible barotropic Euler system is designed and analyzed and its weak convergence to a dissipative measure-valued (DMV) solution [Feireisl et al., Calc. Var. Part. Differ. Equ.55 (2016) 141] of the Euler system is shown. The entropy stability is achieved by introducing a shifted velocity in the convective fluxes of the mass and momentum balances, provided some CFL-like condition is satisfied to ensure stability. A consistency analysis is performed in the spirit of the Lax's equivalence theorem under some physically reasonable boundedness assumptions. The concept of Ƙ-convergence [Feireisl et al., IMA J. Numer. Anal.40 (2020) 2227–2255] is used in order to obtain some strong convergence results, which are then illustrated via rigorous numerical case studies. The convergence of the scheme to a DMV solution, a weak solution and a strong solution of the Euler system using the weak–strong uniqueness principle and relative entropy are presented. [ABSTRACT FROM AUTHOR] |
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