The Jameson’s numerical method for solving the incompressible viscous and inviscid flows by means of artificial compressibility and preconditioning method

A computational code is developed using cell-centered finite volume method with a non-uniform grid for solving the incompressible viscous and inviscid flows. The method has been used to determine the steady incompressible inviscid flows past a cylinder in free stream, the steady incompressible inviscid flows past a circular bump through a channel, and also the steady incompressible viscous flows past a backward facing-step. In this method, the 2D Navier–Stokes equations (or 2D incompressible Euler equations for inviscid flow), which are modified by artificial compressibility and preconditioning concepts, are solved with the Jameson’s artificial dissipation and viscosity terms under the form of a fourth- and second-order x-derivative, respectively. An explicit fourth-order Runge–Kutta integration algorithm is applied to find the steady state condition. The effects of CFL number, artificial viscosity coefficient, and pseudo-compressibility parameter in convergence of solution are investigated.