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

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

2003-09-22

arxiv.org/abs/astro-ph/0309577v1

Astronomy and Astrophysics

Astrophysics

5 pages, 5 figures

Scientific paper

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.

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