scholarly journals IMPLEMENTATION OF A LOW-MACH NUMBER MODIFICATION FOR HIGH-ORDER FINITE-VOLUME SCHEMES FOR ARBITRARY HYBRID UNSTRUCTURED MESHES

2016 ◽  
Author(s):  
Nicholas Simmonds ◽  
Panagiotis Tsoutsanis ◽  
Adrian Gaylard
Keyword(s):  
Mach Number ◽  
Finite Volume ◽  
Unstructured Meshes ◽  
High Order ◽  
Finite Volume Schemes ◽  
Low Mach Number

scholarly journals Low-Mach number treatment for Finite-Volume schemes on unstructured meshes

2018 ◽  
Vol 336 ◽  
pp. 368-393 ◽  
Author(s):  
Nicholas Simmonds ◽  
Panagiotis Tsoutsanis ◽  
Antonis F. Antoniadis ◽  
Karl W. Jenkins ◽  
Adrian Gaylard
Keyword(s):  
Mach Number ◽  
Finite Volume ◽  
Unstructured Meshes ◽  
Finite Volume Schemes ◽  
Low Mach Number

scholarly journals On Low Mach Number Preconditioning of Finite Volume Schemes

PAMM ◽  
2005 ◽  
Vol 5 (1) ◽  
pp. 759-760 ◽  
Author(s):  
Philipp Birken ◽  
Andreas Meister
Keyword(s):  
Mach Number ◽  
Finite Volume ◽  
Finite Volume Schemes ◽  
Low Mach Number

scholarly journals Construction of a low Mach finite volume scheme for the isentropic Euler system with porosity

2021 ◽  
Author(s):  
Pascal Omnes ◽  
Stéphane Dellacherie ◽  
Jonathan Jung
Keyword(s):  
Mach Number ◽  
Finite Volume ◽  
Euler System ◽  
Finite Volume Scheme ◽  
Linear Wave ◽  
Finite Volume Schemes ◽  
Linear Wave Equation ◽  
Continuous Space ◽  
Low Mach Number ◽  
Non Linear System

Classical finite volume schemes for the Euler system  are not accurate at low Mach number and some fixes have to be used and were developed in a vast literature over the last two decades. The question we are interested in in this article is: What about if the porosity is no longer uniform? We first show that this problem may be understood on the linear wave equation taking into account porosity. We explain the influence of the cell geometry on the accuracy property at low Mach number. In the triangular case, the stationary space of the Godunov scheme approaches well enough the continuous space of constant pressure and divergence-free velocity, while this is not the case in the Cartesian case. On Cartesian meshes, a fix is proposed and accuracy at low Mach number is proved to be recovered. Based on the linear study, a numerical scheme and a low Mach fix for the non-linear system, with a non-conservative source term due to the porosity variations, is proposed and tested.

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