Asymptotic preserving IMEX finite volume schemes for low Mach number Euler equations with gravitation

2017 ◽  
Vol 335 ◽  
pp. 222-248 ◽  
Author(s):  
Georgij Bispen ◽  
Mária Lukáčová-Medvid'ová ◽  
Leonid Yelash
Keyword(s):  
Mach Number ◽  
Euler Equations ◽  
Finite Volume ◽  
Finite Volume Schemes ◽  
Asymptotic Preserving ◽  
Low Mach Number

A Comparative Study of Two Preconditioners for Solving 3D Inviscid Low Speed Flows

2011 ◽  
Vol 110-116 ◽  
pp. 423-430 ◽  
Author(s):  
Kazem Hejranfar ◽  
Ramin Kamali Moghadam
Keyword(s):  
Mach Number ◽  
Comparative Study ◽  
Euler Equations ◽  
Finite Volume ◽  
Eigenvalues And Eigenvectors ◽  
Flow Solver ◽  
Low Mach Number ◽  
Euler Flow ◽  
A Cell ◽  
And Performance

In the present study, two preconditioners proposed by Eriksson, and Choi and Merkel are implemented on a 3D upwind Euler flow solver on unstructured meshes. The mathematical formulations of these preconditioning schemes for the set of primitive variables are drawn and their eigenvalues and eigenvectors are compared with each others. A cell-centered finite volume Roe's method is used for discretization of the 3D preconditioned Euler equations. The accuracy and performance of these preconditioning schemes are examined by computing low Mach number flows over the ONERA M6 wing for different conditions.

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.

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 A Weakly Asymptotic Preserving Low Mach Number Scheme for the Euler Equations of Gas Dynamics

2014 ◽  
Vol 36 (6) ◽  
pp. B989-B1024 ◽  
Author(s):  
S. Noelle ◽  
G. Bispen ◽  
K. R. Arun ◽  
M. Lukáčová-Medviďová ◽  
C.-D. Munz
Keyword(s):  
Mach Number ◽  
Euler Equations ◽  
Gas Dynamics ◽  
Asymptotic Preserving ◽  
Low Mach Number ◽  
Equations Of Gas Dynamics

scholarly journals Exact solution and the multidimensional Godunov scheme for the acoustic equations

2022 ◽  
Author(s):  
Wasilij Barsukow ◽  
Christian Klingenberg
Keyword(s):  
Exact Solution ◽  
Mach Number ◽  
Euler Equations ◽  
Two Dimensions ◽  
Finite Volume Scheme ◽  
Godunov Scheme ◽  
Low Mach Number ◽  
Low Mach Number Limit ◽  
Acoustic Equations ◽  
Spatial Dimensions

The acoustic equations derived as a linearization of the Euler equations are a valuable system for studies of multi-dimensional solutions. Additionally they possess a low Mach number limit analogous to that of the Euler equations. Aiming at understanding the behaviour of the multi-dimensional Godunov scheme in this limit, first the exact solution of the corresponding Cauchy problem in three spatial dimensions is derived. The appearance of logarithmic singularities in the exact solution of the 4-quadrant Riemann Problem in two dimensions is discussed. The solution formulae are then used to obtain the multidimensional Godunov finite volume scheme in two dimensions. It is shown to be superior to the dimensionally split upwind/Roe scheme concerning its domain of stability and ability to resolve multi-dimensional Riemann problems. It is shown experimentally and theoretically that despite taking into account multi-dimensional information it is, however, not able to resolve the low Mach number limit.

scholarly journals Convergence of Finite Volume Schemes for the Euler Equations via Dissipative Measure-Valued Solutions

2019 ◽  
Vol 20 (4) ◽  
pp. 923-966 ◽  
Author(s):  
Eduard Feireisl ◽  
Mária Lukáčová-Medvid’ová ◽  
Hana Mizerová
Keyword(s):  
Euler Equations ◽  
Finite Volume ◽  
Finite Volume Schemes
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