Capturing of Shock Wave of Supersonic Flow Over the Bump Channel with TVD, ACM and Jameson Methods

The phenomenon of capturing of sharp gradients, shock waves, and contact discontinuities in compressible aerodynamic flows is the major concern while numerical methods based on the characteristic variables are favorable solutions. The aim of the present study is to introduce a method based on the characteristic variables (Riemann solution) and control the diffusion term in the classic methods in order to capture the shock waves. An efficient blending procedure based on the densitybased algorithm is presented to solve the compressible Euler equations, using a non-orthogonal mesh with collocated finite volume formulation. The fluxes of the convected quantities are approximated by employing the characteristic based total variation diminishing (TVD), artificial compressibility method (ACM) and Jameson methods. Results show that the ACM and TVD methods captured the shock waves with higher resolution than the Jameson method. Moreover, not only quality of shock wave capturing was improved for all flows at the discontinuities by employing ACM and TVD methods, but also the computational time and convergence were improved for the supersonic flows.