Nonlinear error analysis of finite difference solutions of turbulent and unsteady flow fields
Abstract
A computational analysis is performed for the truncation errors incurred in the numerical time integration of the unsteady and/or turbulent NavierStokes equations. The means of analysis is via the modified equation approach. Both the MacCormack explicit and BeamWarming 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 twodimensional NavierStokes equations. Development of the required FORTRAN code for solution of the modified equation is expedited through the use of the symbolic manipulation language, MACSYMA.
 Publication:

Final Report
 Pub Date:
 May 1988
 Bibcode:
 1988ncsu.rept.....M
 Keywords:

 Finite Difference Theory;
 Flow Distribution;
 NavierStokes Equation;
 Numerical Analysis;
 Supersonic Flow;
 Turbulent Flow;
 Unsteady Flow;
 Computation;
 Error Analysis;
 Fortran;
 Nonlinear Equations;
 Nonlinearity;
 Numerical Integration;
 Programming Languages;
 Solutions;
 Symbolic Programming;
 Time;
 Truncation Errors;
 Fluid Mechanics and Heat Transfer