A method for relaxing the CFL-condition in time explicit schemes

Abstract

A method for relaxing the CFL-condition, which limits the time step size in explicit methods in computational fluid dynamics, is presented. The method is based on re-formulating explicit methods in matrix form, and considering them as a special-Jacobi iteration scheme that converge efficiently if the CFL- number is less than unity. By adopting this formulation, one can design various solution methods in arbitrary dimensions that range from explicit to unconditionally stable implicit methods in which CFL-number could reach arbitrary large values. In addition, we find that adopting a specially varying time stepping scheme accelerates convergence toward steady state solutions and improves the efficiently of the solution procedure.