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.

Numerical Simulation and Experimental Studies on Aft Hull Local Parameterized Non-Geosim Deformation for Correcting Scale Effects of Nominal Wake Field

“…The grid refineme nt factor for the fine/medium-1 (medium-1/medium-2, medium-2/coarse, coarse/very coarse) grids is 1.32, 1.18, 1.27 and 1.12, respectively. The grid refinement ratio of fine to medium (medium to coarse) grids is approximately 1.2, which is consistent with Roy et al [34].A comparison of the differences among the five mesh scenarios can be obtained from the perspectives of the resistance coefficient and wake field distribution.…”

“…In general, the definition of G r is the ratio of coarse to fine cell sizes, indicating that the refinement factor is simple to compute for structured grid. However, in the present study, Cartesian cut-cell method was used to generate the computational mesh, the refinement ratio G r was considered as follows [34]:…”

“…Roy et al [34] presented methods for assessing the uniformity of the grid refinement with Cartesian grid. As a result, five grid systems considered in the present study was constructed based on method of Roy et al [34] to unifor mly refine the grid over the entire domain in all three coordinate directions. The grid refineme nt factor for the fine/medium-1 (medium-1/medium-2, medium-2/coarse, coarse/very coarse) grids is 1.32, 1.18, 1.27 and 1.12, respectively.…”

Effects of the advance ratio on the evolution of a propeller wake

“…Roy et al [27] presented methods for assessing the uniformity of the grid refinement with Cartesian grid. As a result, three grid systems considered in the present study was constructed based on method of Roy et al [27] to uniformly refine the grid over the entire domain in all three coordinate directions.…”

“…Roy et al [27] presented methods for assessing the uniformity of the grid refinement with Cartesian grid. As a result, three grid systems considered in the present study was constructed based on method of Roy et al [27] to uniformly refine the grid over the entire domain in all three coordinate directions. For three grids discussed above, the grid refinement ratio of fine to medium (medium to coarse) grids is approximately 1.2, which is consistent with Roy et al [27].…”