scholarly journals Study of a New Asymptotic Preserving Scheme for the Euler System in the Low Mach Number Limit

2017 ◽  
Vol 39 (5) ◽  
pp. A2099-A2128 ◽  
Author(s):  
Giacomo Dimarco ◽  
Raphaël Loubère ◽  
Marie-Hélène Vignal
Keyword(s):  
Mach Number ◽  
Euler System ◽  
Asymptotic Preserving ◽  
Low Mach Number ◽  
Low Mach Number Limit ◽  
Asymptotic Preserving Scheme

Incompressible limit for the two-dimensional isentropic Euler system with critical initial data

2014 ◽  
Vol 144 (6) ◽  
pp. 1127-1154 ◽  
Author(s):  
Taoufik Hmidi ◽  
Samira Sulaiman
Keyword(s):  
Mach Number ◽  
Initial Data ◽  
Euler System ◽  
Incompressible Limit ◽  
Two Dimensional ◽  
Low Mach Number ◽  
Low Mach Number Limit ◽  
Critical Besov Space ◽  
Convergence Results ◽  
Incompressible Euler

We study the low-Mach-number limit for the two-dimensional isentropic Euler system with ill-prepared initial data belonging to the critical Besov space . By combining Strichartz estimates with the special structure of the vorticity, we prove that the lifespan of the solutions goes to infinity as the Mach number goes to zero. We also prove strong convergence results of the incompressible parts to the solution of the incompressible Euler system.

scholarly journals A homogeneous relaxation low Mach number model

2021 ◽  
Author(s):  
Gloria Faccanoni ◽  
Bérénice Grec ◽  
Yohan Penel
Keyword(s):  
Fluid Flow ◽  
Mach Number ◽  
Equation Of State ◽  
Specific Model ◽  
Relaxation Model ◽  
Two Phase ◽  
Asymptotic Preserving ◽  
Low Mach Number ◽  
Asymptotic Preserving Scheme ◽  
Phase Fluid

In the present paper, we investigate a new homogeneous relaxation model describing the behaviour of a two-phase fluid flow in a low Mach number regime, which can be obtained as a low Mach number approximation of the well-known HRM. For this specific model, we derive an equation of state to describe the thermodynamics of the two-phase fluid. We prove some theoretical properties satisfied by the solutions of the model, and provide a well-balanced scheme. To go further, we investigate the instantaneous relaxation regime, and prove the formal convergence of this model towards the low Mach number approximation of the well-known HEM. An asymptotic-preserving scheme is introduced to allow numerical simulations of the coupling between spatial regions with different relaxation characteristic times.

scholarly journals Incompressible limit of Euler equations with damping

2021 ◽  
Vol 30 (1) ◽  
pp. 126-139
Author(s):  
Fei Shi ◽  
Keyword(s):  
Cauchy Problem ◽  
Mach Number ◽  
Euler System ◽  
Existence Results ◽  
Incompressible Limit ◽  
Low Mach Number ◽  
Uniform Estimates ◽  
Low Mach Number Limit ◽  
Compressible Euler ◽  
The Cauchy Problem

<abstract><p>The Cauchy problem for the compressible Euler system with damping is considered in this paper. Based on previous global existence results, we further study the low Mach number limit of the system. By constructing the uniform estimates of the solutions in the well-prepared initial data case, we are able to prove the global convergence of the solutions in the framework of small solutions.</p></abstract>

scholarly journals On the Low Mach Number Limit for the Compressible Euler System

2019 ◽  
Vol 51 (2) ◽  
pp. 1496-1513 ◽  
Author(s):  
Eduard Feireisl ◽  
Christian Klingenberg ◽  
Simon Markfelder
Keyword(s):  
Mach Number ◽  
Euler System ◽  
Low Mach Number ◽  
Low Mach Number Limit ◽  
Compressible Euler

scholarly journals Low Mach number limit for a model of accretion disk

2018 ◽  
Vol 38 (7) ◽  
pp. 3239-3268 ◽  
Author(s):  
Donatella Donatelli ◽  
◽  
Bernard Ducomet ◽  
Šárka Nečasová ◽  
◽  
...  
Keyword(s):  
Mach Number ◽  
Accretion Disk ◽  
Low Mach Number ◽  
Low Mach Number Limit

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.

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