A Numerical Method for the Solution of Compressible and Incompressible Fluid Flows

Abstract

Numerical simulation plays nowadays an important role to predict the flow field in many situations. To design a new mechanical device involving fluid dynamics, a numerical simulation is well accepted and justified. However, many work still remains to improve the numerical methods towards a fast, accurate and stable convergence. This work presents efficiency studies to solve compressible and
incompressible fluid flows using a finite-volume, explicit Runge-Kutta multistage scheme, with central spatial discretization in combination with multigrid. An extension of the methodology normally employed to solve compressible flows is used to solve incompressible flow problems. Numerical results are presented for a cylinder and the NACA 0012 airfoil for Mach-numbers ranging from 0.8 to 0.005 using the Euler equations.