ASYMPTOTIC PRESERVING ERROR ESTIMATES FOR NUMERICAL SOLUTIONS OF COMPRESSIBLE NAVIER-STOKES EQUATIONS IN THE LOW MACH NUMBER REGIME

作者：Feireisl Eduard; Lukacova Medvid'ova Maria; Necasova Sarka; Novotny Antonin; She Bangwei^*

来源：Multiscale Modeling and Simulation, 2018, 16(1): 150-183.

DOI：10.1137/16M1094233

• Navier-Stokes system
• finite element numerical method
• finite volume numerical method
• error estimates
• asymptotic preserving schemes
• low Mach number

We study the convergence of numerical solutions of the compressible Navier-Stokes system to its incompressible limit. The numerical solution is obtained by a combined finite element-finite volume method based on the linear Crouzeix-Raviart finite element for the velocity and piece wise constant approximation for the density. The convective terms are approximated using upwinding. The distance between a numerical solution of the compressible problem and the strong solution of the incompressible Navier-Stokes equations is measured by means of a relative energy functional. For barotropic pressure exponent gamma >= 3/2 and for well-prepared initial data we obtain uniform convergence of order O(root Delta t, h(a,) epsilon), alpha = min{2 gamma-3/gamma, 1}. Extensive numerical simulations confirm that the numerical solution of the compressible problem converges to the solution of the incompressible Navier-Stokes equations as the discretization parameters Delta t, h and the Mach number epsilon tend to zero.

• 出版日期2018