Quantification and Reduction of Numerical Uncertainties by Improvement of the TAU Grid Adaptation Tool and Adjoint Methods

Abstract

Within the framework of the project MUNA, several enhancements of the grid adaptation tool of the DLR TAU Code were prepared, implemented and tested. Therefore, various quality aspects of the single elements of the computational grid were investigated and used to modify the adapted grids. Conditions for the decomposability of the elements are evaluated and used for a more accurate compliance of the point density with the requirement of the error indicator in the grid refinement. Geometrical element quality terms for the element types of the TAU Code are derived from the known mean-ratio element quality measure for a simplex and used to avoid the worst shaped elements in an adapted grid. In addition, the TAU adaptation was extended to use the sensors provided by the adjoint solver of TAU as an error indicator for a goal orientated grid adaptation. The results are compared to that of a simple differences-based grid adaptation. Furthermore, the adjoint method was used for the efficient quantification of uncertainties in the aerodynamic coefficients caused by variations of the parameters of the SAE and the Wilcox-k-ω turbulence model.