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

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