Grid Generation

_{Funded by NASA Ames, Lewis/Glenn, Ford, GM, DaimlerChrysler, DOE; students: Julio Dulce, Robert Bailey, Erlendur Steinthorrson, Mark Stephens, Mark Rimlinger, Xubin Gu, Xuehui “Christine” Qin, Xingkai “Kyle” Chi, Brandon Williams}.

Grid generation is important to CFD because without a good grid or mesh, one cannot generate a high-quality CFD solution. Also, grid generation is the most time-consuming part of CFD and requires a high-level of user expertise on CFD and in understanding the problem being studied because the grid/mesh and the flow physics are intimately connected.

Contributions made include:

1. Developed a highly efficient and versatile algebraic surface generator (referred to as 3-D bidirectional Hermite interpolation) that ensures C1 continuity across patches without the need to solve systems of equations. This method is ideal for time-dependent problems with moving and deforming geometries, and was applied to study the flow fields in the combustion chambers of reciprocating piston and Wankel rotary engines.
2. Developed several techniques to enhance control of grid-point distribution in algebraic grid generation methods based on transfinite interpolation, including orthogonality of grid lines at boundaries and smoothness in r-refinement.
3. Developed a code called GRID2D/3D to generate grid systems in complex-shaped two- and three-dimensional spatial domains that can deform in time and be single- or multi-block.
4. Developed a knowledge-based automatic grid generator involving patched/overlapped grids for CFD analyses of shock-wave/boundary-layer interactions with bleed through rows of circular holes (this tool can be used by non-experts in CFD to generate high-quality grids along with all other inputs needed to generate a solution in the OVERFLOW code in seconds).
5. Developed grid-quality measures for structured and unstructured meshes that take into account the vector and tensor nature of CFD solutions as well as the geometry/shape of the cells in the mesh and showed their correlation to errors in the computed solutions.
6. Developed the concept and the formulation of the discrete-error-transport equation (DETE) for estimating grid-induced errors in steady and unsteady CFD solutions.
7. Developed an efficient solution-adaptive mesh refinement strategy based on the concept that error source and error location may not coincide.
8. Developed a method to generate “smooth” high quality grids for rough surfaces with discontinuities in the boundary geometry such as iced airfoils and wings by using algebraic grid generation with partial elliptic smoothing (methods developed were incorporated into NASA’s SmagICE code).