Aspects of Numerical Uncertainties in Time Marching to Steady-State Numerical Solutions

Abstract

Knowledge from recent advances in the understanding of global nonlinear behavior of numerical schemes is employed to isolate some aspects of numerical uncertainties in time-marching approaches to obtain steady-state numerical solutions. Strong dependence on initial data and the permissibility of spurious steady-state numerical solutions, stabilization of unstable steady states by implicit time discretizations, and convergence properties and spurious behavior of high-resolution shock-capturing schemes are discussed and illustrated with examples. The goal is to illustrate the important role that global nonlinear behavior of numerical schemes can play in minimizing sources of numerical uncertainties in computational fluid dynamics.