An Asymptotic-Preserving all-speed scheme for the Euler and Navier-Stokes equations

作者：Cordier Floraine; Degond Pierre^*; Kumbaro Anela

来源：Journal of Computational Physics, 2012, 231(17): 5685-5704.

DOI：10.1016/j.jcp.2012.04.025

• Low Mach number limit
• Asymptotic-Preserving
• All-speed
• Compressible flows
• Incompressible flows
• Navier-Stokes equations
• Euler equations

We present an Asymptotic-Preserving %26apos;all-speed%26apos; scheme for the simulation of compressible flows valid at all Mach-numbers ranging from very small to order unity. The scheme is based on a semi-implicit discretization which treats the acoustic part implicitly and the convective and diffusive parts explicitly. This discretization, which is the key to the Asymptotic-Preserving property, provides a consistent approximation of both the hyperbolic compressible regime and the elliptic incompressible regime. The divergence-free condition on the velocity in the incompressible regime is respected, and an the pressure is computed via an elliptic equation resulting from a suitable combination of the momentum and energy equations. The implicit treatment of the acoustic part allows the time-step to be independent of the Mach number. The scheme is conservative and applies to steady or unsteady flows and to general equations of state. One and two-dimensional numerical results provide a validation of the Asymptotic-Preserving %26apos;all-speed%26apos; properties.

• 出版日期2012-7-1
• 单位中国地震局