초록
This paper presents a unified approach to artificial compressibility and local low Mach number preconditioning methods. The numerical formulation is presented, which provides a seamless transition between incompressible and compressible systems. A single preconditioner that can act as the artificial compressibility or the local preconditioning under a given Mach number condition is derived. An artificial compressibility method is proposed for the unified system. The unified preconditioner is applied to the upwind approach, Roe’s approximate Riemann solver, and the JST artificial dissipation approach. A Roe average, which can be applied to the unified systems in a single form is derived. The preconditioning matrix is applied to a single solver to analyze problems ranging from incompressible fluid flows to compressible flows with shocks.
