scholarly journals Low Mach Number Limit of Full Compressible Navier–Stokes Equations with Revised Maxwell Law

2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Zhao Wang ◽  
Yuxi Hu
Keyword(s):  
Mach Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Mach Number ◽  
Low Mach Number Limit

scholarly journals On the Low Mach Number Limit for Quantum Navier--Stokes Equations

2020 ◽  
Vol 52 (6) ◽  
pp. 6105-6139
Author(s):  
Paolo Antonelli ◽  
Lars Eric Hientzsch ◽  
Pierangelo Marcati
Keyword(s):  
Mach Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Mach Number ◽  
Low Mach Number Limit

Adjoint algorithms for the Navier–Stokes equations in the low Mach number limit

2012 ◽  
Vol 231 (4) ◽  
pp. 1900-1916 ◽  
Author(s):  
Gary J. Chandler ◽  
Matthew P. Juniper ◽  
Joseph W. Nichols ◽  
Peter J. Schmid
Keyword(s):  
Mach Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Mach Number ◽  
Low Mach Number Limit

scholarly journals Implicit MAC scheme for compressible Navier–Stokes equations: low Mach asymptotic error estimates

2020 ◽  
Author(s):  
David Maltese ◽  
Antonín Novotný
Keyword(s):  
Mach Number ◽  
Initial Data ◽  
Error Estimate ◽  
Strong Solution ◽  
Stokes Equations ◽  
Main Tool ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Mach Number ◽  
Mac Scheme

Abstract We investigate the error between any discrete solution of the implicit marker-and-cell (MAC) numerical scheme for compressible Navier–Stokes equations in the low Mach number regime and an exact strong solution of the incompressible Navier–Stokes equations. The main tool is the relative energy method suggested on the continuous level in Feireisl et al. (2012, Relative entropies, suitable weak solutions, and weak–strong uniqueness for the compressible Navier–Stokes system. J. Math. Fluid Mech., 14, 717–730). Our approach highlights the fact that numerical and mathematical analyses are not two separate fields of mathematics. The result is achieved essentially by exploiting in detail the synergy of analytical and numerical methods. We get an unconditional error estimate in terms of explicitly determined positive powers of the space–time discretization parameters and Mach number in the case of well-prepared initial data and in terms of the boundedness of the error if the initial data are ill prepared. The multiplicative constant in the error estimate depends on a suitable norm of the strong solution but it is independent of the numerical solution itself (and of course, on the discretization parameters and the Mach number). This is the first proof that the MAC scheme is unconditionally and uniformly asymptotically stable in the low Mach number regime.

scholarly journals Splitting methods for low Mach number Euler and Navier-Stokes equations

1989 ◽  
Vol 17 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Saul Abarbanel ◽  
Pravir Duth ◽  
David Gottlieb
Keyword(s):  
Mach Number ◽  
Stokes Equations ◽  
Splitting Methods ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Mach Number
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