Estimation of Numerical Error for 3D Inviscid Flows on Cartesian Grids

Abstract

The two primary sources of numerical error in CFD simulations are iterative error and discretization error. These errors are examined for inviscid aerodynamic computations of a slender missile configuration using Cartesian grids. A new iterative error estimator is proposed which incorporates both exponential and oscillatory convergence behavior. This iterative error estimator is discussed in detail and used to estimate the iterative error in the yaw and drag force histories. Discretization errors are analyzed using uniform grid refinement and Richardson extrapolation. Methods for assessing the uniformity of the grid refinement with Cartesian grid methods are presented and the convergence behavior of the aerodynamic forces and moments is discussed. While the forces and moments do not converge at the formal order of accuracy of two, conservative discretization error estimates show that the forces are reasonably well converged with generally less than 5% error, the pitching moments are converged to within 20%, and rolling moment gives error estimates as high as a factor of three.