A fast transient solver for low-Mach number aerodynamics and aeroacoustics

The fractional step method is an efficient time advancement scheme for problems involving transient incompressible flow. The method is desirable over traditional SIMPLE-like algorithms for its non-iterative nature. This paper presents a technique that extends the fractional step method to low-Mach number compressible flow problems. The proposed pressure-velocity coupling and a transient SIMPLEC algorithm are validated and verified for a 1D acoustic wave propagation and a convective isentropic vortex to qualitatively evaluate their convergence properties. Next, both algorithms are used to predict aerodynamic and aeroacoustic behaviour of flow past a wall-mounted side mirror. The proposed scheme is stable at acoustic CFL number greater than one, and at convective Co number equal one. The L₂ error norms of both schemes exhibit second order accuracy as grids are refined, while the new scheme requires significantly less computation effort for an equal error. The new fractional step method consumes only 20% to 35% of the computation effort that is required by the transient SIMPLEC algorithm for the same error, and is easily scalable to a greater number of CPU processors.