scholarly journals An entropy satisfying two-speed relaxation system for the barotropic Euler equations: application to the numerical approximation of low Mach number flows

2020 ◽  
Vol 145 (1) ◽  
pp. 35-76 ◽  
Author(s):  
François Bouchut ◽  
Christophe Chalons ◽  
Sébastien Guisset
Keyword(s):  
Mach Number ◽  
Euler Equations ◽  
Numerical Approximation ◽  
Low Mach Number ◽  
Relaxation System ◽  
Entropy Satisfying

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 A Hybrid Adaptive Low-Mach-Number/Compressible Method for the Euler Equations

2017 ◽  
Author(s):  
Emmanuel Motheau ◽  
Max Duarte ◽  
Ann S. Almgren ◽  
John B. Bell
Keyword(s):  
Mach Number ◽  
Euler Equations ◽  
Low Mach Number

scholarly journals A hybrid adaptive low-Mach number/compressible method: Euler equations

2018 ◽  
Vol 372 ◽  
pp. 1027-1047 ◽  
Author(s):  
Emmanuel Motheau ◽  
Max Duarte ◽  
Ann Almgren ◽  
John B. Bell
Keyword(s):  
Mach Number ◽  
Euler Equations ◽  
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 Calculation of low Mach number acoustics: a comparison of MPV, EIF and linearized Euler equations

2005 ◽  
Vol 39 (3) ◽  
pp. 561-576 ◽  
Author(s):  
Sabine Roller ◽  
Thomas Schwartzkopff ◽  
Roland Fortenbach ◽  
Michael Dumbser ◽  
Claus-Dieter Munz
Keyword(s):  
Mach Number ◽  
Euler Equations ◽  
Low Mach Number ◽  
Linearized Euler Equations
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