Error estimates for the implicit MAC scheme for the compressible Navier-Stokes equations
type: Item
instance of: scholarly article
title: Error estimates for the implicit MAC scheme for the compressible Navier-Stokes equations
zbMATH Open document ID: 1412.35253
author: David Maltese
author: Antonín Novotný
author: T. Gallouët
published in: Numerische Mathematik
publication date: 2019-02-08T00:00:00Z
review text: The authors consider the implicit Marker-And-Cell scheme (MAC scheme in short) for the compressible Navier-Stokes equations. Unconditional error estimates for a class of staggered schemes interesting from the point of view of mathematical simulations in two and three dimensional problems are derived. These are obtained using the discrete version of the relative energy method introduced on the continuous level in [\textit{E. Feireisl} et al., J. Math. Fluid Mech. 14, No. 4, 717--730 (2012; Zbl 1256.35054)], and involve the deep theoretical analysis of the continuous versions in combination with the numerical tools. This error estimate does not use stability hypotheses on the solution of the numerical scheme.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 76M12
Mathematics Subject Classification ID: 76M20
zbMATH DE Number: 7017850
zbMATH Keywords: Navier-Stokes system
zbMATH Keywords: compressible
zbMATH Keywords: barotropic
zbMATH Keywords: MAC scheme
zbMATH Keywords: error estimates
describes a project that uses: CALIF3S
MaRDI profile type: Publication
full work available at URL: s00211-018-1007-x
OpenAlex ID: W2901822098
cites work: An L2-stable approximation of the Navier-Stokes convection operator for low-order non-conforming finite elements
cites work: A unified method for computing incompressible and compressible flows in boundary-fitted coordinates
cites work: Error estimate for time-explicit finite volume approximation of strong solutions to systems of conservation laws
cites work: Pressure method for the numerical solution of transient, compressible fluid flows
cites work: A projection method for low speed flows
cites work: Q5185568
cites work: Éléments finis: théorie, applications, mise en œuvre.
cites work: Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes
cites work: Finite volume methods
cites work: A convergent finite element-finite volume scheme for the compressible Stokes problem. Part II: the isentropic case
cites work: Q5702675
cites work: Error estimates for a numerical method for the compressible Navier–Stokes system on sufficiently smooth domains
cites work: Relative entropies, suitable weak solutions, and weak-strong uniqueness for the compressible Navier-Stokes system
cites work: Convergence of a mixed finite element-finite volume scheme for the isentropic Navier-Stokes system via dissipative measure-valued solutions
cites work: On the existence of globally defined weak solutions to the Navier-Stokes equations
cites work: Weak-strong uniqueness property for the full Navier-Stokes-Fourier system
cites work: Suitable weak solutions to the Navier-Stokes equations of compressible viscous fluids
cites work: Numerical approximation of the general compressible Stokes problem
cites work: An unconditionally stable finite element-finite volume pressure correction scheme for the drift-flux model
cites work: W\(^{1,q }\) stability of the Fortin operator for the MAC scheme
cites work: Convergence of the marker-and-cell scheme for the incompressible Navier-Stokes equations on non-uniform grids
cites work: Error estimates for a numerical approximation to the compressible barotropic Navier–Stokes equations
cites work: Staggered discretizations, pressure correction schemes and all speed barotropic flows
cites work: Numerical calculation of almost incompressible flow
cites work: A numerical fluid dynamics calculation method for all flow speeds
cites work: Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface
cites work: Conservativity and weak consistency of a class of staggered finite volume methods for the Euler equations
cites work: Stability and consistency of a finite difference scheme for compressible viscous isentropic flow in multi-dimension
cites work: Solution of the implicitly discretized fluid flow equations by operator- splitting
cites work: The computation of compressible and incompressible recirculating flows by a non-iterative implicit scheme
cites work: Finite-volume schemes for Friedrichs systems in multiple space dimensions:A priori anda posteriori error estimates
cites work: A convergent FEM-DG method for the compressible Navier-Stokes equations
cites work: Q4389323
cites work: Q3159147
cites work: Simple nonconforming quadrilateral Stokes element
cites work: Navier-Stokes equations for compressible fluids: Global existence and qualitative properties of the solutions in the general case
cites work: Stability analysis of segregated solution methods for compressible flow
cites work: A conservative pressure-correction method for flow at all speeds.
cites work: A superlinearly convergent Mach-uniform finite volume method for the Euler equations on staggered unstructured grids
cites work: Convergence of an explicit finite volume scheme for first order symmetric systems
cites work: A semi-implicit method for resolution of acoustic waves in low Mach number flows
cites work: A Mach-uniform unstructured staggered grid method
cites work: Q4518447
cites work: Q3184890
DOI: 10.1007/S00211-018-1007-X
Wikidata QID: Q128989273
description: scientific article; zbMATH DE number 7017850