Low Mach preconditioned non-reflecting boundary conditions for the harmonic balance solver

Abstract

In CFD, unsteady computations are cost-intensive. The HB method represents a cost-efficient alternative. Here, for time-periodic flows, the governing equations are recasted in the Fourier domain. In the low Mach regime, the compressible governing equations are stiff. Therefore, density-based solvers converge slowly. Low Mach preconditioning equalizes the eigenvalues of the system of equations, to improve the condition number and remove the stiffness of the system. In this paper, low Mach preconditioning is applied to the HB method, with emphasis on the NRBCs. These boundary conditions have a crucial impact on the flow inside the truncated computational domains used in CFD. Improper boundary conditions reflect waves exiting the computational domain and deteriorate the quality of the solution. However,NRBCs avoid spurious reflections. We explain that to precondition the NRBC its formulation in terms of characteristics has to be adapted. An academic wave propagation test case is computed for different wave configurations to validate the preconditioned boundary conditions. The use of non-preconditioned NRBCs in a preconditioned computation leads to instabilities and reflections at the boundaries of the domain. A consistent setup with preconditioned NRBCs improves the stability and leads to good non-reflecting properties for all presented wave configurations.