Nonlinear Error Analysis of Finite Difference Solutions of Turbulent and Unsteady Flow Fields

摘要

A computational analysis is performed for the truncation errors incurred in the numerical time integration of the unsteady and/or turbulent Navier-Stokes equations. The means of analysis is via the modified equation approach. Both the MacCormack explicit and Beam-Warming implicit numerical methods are considered. A simplified analysis applied to Burger's equation indicates that the leading order term is both dissipative and dispersive. The modified equation is derived for the aforementioned explicit and implicit methods as applied to the full two-dimensional Navier-Stokes equations. Development of the required Fortran code for solution of the modified equation is expedited through the use of the symbolic manipulation language, MACSYMA. Keywords: Programming languages, Turbulent flow, Supersonic flow. (edc)