Zero Mach number limit of the compressible Navier–Stokes–Korteweg equations

2016 ◽  
Vol 14 (1) ◽  
pp. 233-247 ◽  
Author(s):  
Yeping Li ◽  
Wen-An Yong
Keyword(s):  
Mach Number ◽  
Navier Stokes ◽  
Zero Mach Number Limit

scholarly journals Fujita–Kato solution for compressible Navier–Stokes equations with axisymmetric initial data and zero Mach number limit

2019 ◽  
Vol 22 (05) ◽  
pp. 1950041
Author(s):  
Boris Haspot
Keyword(s):  
Mach Number ◽  
Initial Data ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Small Initial Data ◽  
Dimension Formula ◽  
Global Strong Solution ◽  
Rotational Part ◽  
Zero Mach Number Limit

In this paper, we investigate the question of the existence of global strong solution for the compressible Navier–Stokes equations for small initial data such that the rotational part of the velocity [Formula: see text] belongs to [Formula: see text] (in dimension [Formula: see text]). We show then an equivalent of the so-called Fujita–Kato theorem to the case of the compressible Navier–Stokes equations when we consider axisymmetric initial data. The main difficulty is linked to the fact that in this case the velocity is not Lipschitz, as a consequence we have to study carefully the coupling between the rotational and irrotational part of the velocity. In a second part, we address the question of convergence to the incompressible model (for ill-prepared initial data) when the Mach number goes to zero.

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.

FLOWS OF VISCOUS COMPRESSIBLE FLUIDS UNDER STRONG STRATIFICATION: INCOMPRESSIBLE LIMITS FOR LONG-RANGE POTENTIAL FORCES

2011 ◽  
Vol 21 (01) ◽  
pp. 7-27 ◽  
Author(s):  
EDUARD FEIREISL
Keyword(s):  
Mach Number ◽  
Acoustic Waves ◽  
Stokes System ◽  
Hybrid Methods ◽  
Singular Limit ◽  
Acoustic Energy ◽  
Compressible Fluids ◽  
Navier Stokes ◽  
Whole Space ◽  
Rage Theorem

We study the singular limit of the compressible Navier–Stokes system in the whole space ℝ3, where the Mach number and Froude number are proportional to a small parameter ε → 0. The central issue is the local decay of the acoustic energy proved by means of the RAGE theorem. The result is quite general and the proposed approach can be applied to a large variety of problems that concern propagation of acoustic waves in compressible fluids. In particular, the method can be used for showing stability of various numerical schemes based on the so-called hybrid methods.

A 3-D Thin Layer Navier-Stokes Code for Supersonic Laminar and Turbulent Flows

2002 ◽  
Author(s):  
Omid Abouali ◽  
Mohammad M. Alishahi ◽  
Homayoon Emdad ◽  
Goodarz Ahmadi
Keyword(s):  
Experimental Data ◽  
Shock Wave ◽  
Mach Number ◽  
Turbulent Flows ◽  
Turbulence Modeling ◽  
Cross Flow ◽  
Navier Stokes ◽  
Cross Sectional ◽  
Laminar And Turbulent Flows ◽  
Circumferential Pressure

A 3-D Thin Layer Navier-Stokes (TLNS) code for solving viscous supersonic flows is developed. The new code uses several numerical algorithms for space and time discretization together with appropriate turbulence modeling. Roe’s method is used for discretizing the convective terms and the central differencing scheme is employed for the viscous terms. An explicit time marching technique and a finite volume space discretization are used. The developed computational model can handle both laminar and turbulent flows. The Baldwin-Lomax model and Degani-Schiff modifications are used for turbulence modeling. The computational model is applied to a hypersonic laminar flow at Mach 7.95 around a cone at different incidence angles. The circumferential pressure distribution is compared with the experimental data. The cross-sectional Mach number contours are also presented. It is shown that in addition to the outer shock, a cross-flow shock wave is also present in the flow field. The cases of supersonic turbulent flows with Mach number 3 around a tangent-ogive with incidence angles of 6° and a secant-ogive with incidence angles of 10° are also studied. The circumferential pressure distributions are compared with the experimental data and the Euler code results and good agreement is obtained. The cross-sectional Mach number contours are also presented. It is shown that in this case also in addition to the outer shock, a cross-flow shock wave is also present at the incidence angle of 10°.

Sign in / Sign up

Export Citation Format

Share Document