scholarly journals Global existence and low Mach number limit to a 3D compressible micropolar fluids model in a bounded domain

2017 ◽  
Vol 37 (6) ◽  
pp. 3423-3434 ◽  
Author(s):  
Jingrui Su ◽  
Keyword(s):  
Mach Number ◽  
Global Existence ◽  
Bounded Domain ◽  
Micropolar Fluids ◽  
Low Mach Number ◽  
Low Mach Number Limit

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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