Solution of Incompressible and Compressible Fluid Flows Based on Runge-Kutta Time-Stepping Schemes

Abstract

The great development of numerical cak:u1ation lead to a variety of methods, which are different in their solution algorithms as well as in the discretization of the governing
equations. Although this development, many work still remains to improve them towards a fast, accurate and stahle convergence. This worle employs a numerical method to solve compressible and incompressible fluid flows using a finite-volume, explicit Runge-Kutta
multistage scheme, with central spatial discretization in combination with multigrid and preconditioning. The discretization used follows the ceII- and node-centered arrangement of the control volume and update points for the Bow variables. Numerical results are presented for NACA 0012 airfoil and a three dimensional channel for the Euler equations. Mach number is varied between 0.8 and 0.002.