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

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 CFLnumber 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.