All-speed Two-phase Computations for General Equation of State with Preconditioning Techniques and Scaling of Numerical Dissipations

Abstract

The present research focuses on the system preconditioning and the scaling of numerical dissipations of RoeM and AUSMPW+ methods to enable more efficient and accurate computations of all-speed two-phase flows. Previous all-speed two-phase RoeM and AUSMPW+ methods have applied only steady system preconditioning technique while unsteady system preconditioning is essential for the convergence acceleration of unsteady low Mach number flows. In this study, unsteady system preconditioning is achieved by the consideration of Strouhal number in preconditioning parameter. Unlike existing preconditioning techniques, scaling factors in numerical dissipations are treated separately with preconditioning parameter in system so that the numerical instability and the accuracy degradation issues in low Mach number regions are resolved regardless of the convergence. The extension of two-phase RoeM and AUSMPW+ methods to general equation of state (EOS) is completed through the modification of shock discontinuity sensing term (SDST) to be independent on EOS. The performance of the modified SDST is confirmed to be as stable as the previous SDST which works well, but is compatible only with specific forms of EOS.