Using of Turkel precondition method for convergence acceleration of compressible flow with low Mach number

The system of compressible equations using upstream numerical methods has convergence problem to analyze low-Mach number flow. In this study precondition method is employed in Euler equations to solve convergence problem in low-Mach number flow and this preconditioned equations are used to analyze flow around a two-dimensional body. The preconditioner modifies the transient behavior of the Euler equations in manner that the stiffness of the eigenvalues is removed and allows for a faster convergence to the steady state. So, Turkel precondition method, one of the useful preconditioner matrices, is applied in system of Euler equations. As majority of solvers use conservative variables, precondition matrix is recalculated for conservative variables and is employed in Euler equations. The upstream finite volume Roe method in an unstructured grid is employed for space discretization of equations. Transient part of equations also is discretized with fourth order explicit Runge-Kutta method. The performance of the proposed approach is vetted through an inviscid tow-dimensional flow around the NACA0012 airfoil with different Mach number and the steady state solution is calculated. Numerical results showý that Turkel preconditioner allow for a faster convergence to the steady state solution in low-Mach number. . .