Shock capturing method by numerical dissipation control on symmetric airfoil

In this paper, an efficient procedure based on the density-based algorithm with explicit solver is presented to solve the compressible Euler equations on a non-orthogonal mesh with finite volume formulation and The fluxes of the convected quantities including mass flow rate are approximated by using the characteristic based TVD and ACM and Jameson methods. the aim of the present study is to introduce a method based on the characteristic variables (Riemann solution) and control of the diffusion term in the classic methods in order to capture the shock waves. Hereby, an inviscid supersonic flow is solved and results are compared together in view of resolution and accuracy of shock waves capturing, and solution convergence. In this paper, the convergence target for mass equations and momentum equations is decrement of residuals from 10-6. Results show in density-based algorithm the characteristics velocities are better converged due to the augmentation of limiter, ACM and TVD methods capture the shock waves with higher resolution relative to the Jameson method. Shock waves include simple waves reflected waves, and waves interaction. Also the ACM method is a useful technique, which prevents the smearing of discontinuities and improves the resolution of shocks and accelerates the convergence rate of the solution in the supersonic flows .