An investigation of the healing strategies of the numerical dissipation of spectrum AUSM-family toward steady low Mach flows

In this research, a spectrum variety of AUSM-family, including AUSM+, AUSM+UP, SLAU, and AUSM+M, in a numerical framework, based on the finite volume method to solve preconditioned two-dimensional Eulerian equations, was developed in an unstructured grid and the performance of this family has been investigated in incompressible flow. Where fluid velocity is low, convergence rate of density base solvers is distorted. Turkle's preconditioning method based on the conservation variable has been utilized to remedy the poor convergence at low speeds flows. In addition, at low speeds, the imbalance between the elements in this family's convective and pressure fluxes results in a deterioration of accuracy. Therefore, the necessary mathematical literature has been developed to solve the imbalance problem raised at the low speeds of the AUSM family. In addition, to further accelerate the convergence rate and reduce the stiffness of the equations at low speeds, the time part of the equations has been discretized utilizing the modified second-order Bashforth-Moulton method. To investigate the accuracy and efficiency of the developed AUSM family, steady two-dimensional inviscid tests around the NACA0012 airfoil, three-element 30P-30N airfoil, and half-cylindrical have been constructed for a wide range of low and highly- low Mach numbers. The results show no optimal trade-off between convergence rate and accuracy improvement within AUSM family. The accuracy improvement is not accompanied by reduced convergence time necessarily in low velocity flow field.