Green-Gauss/Weighted-Least-Squares Hybrid Gradient Reconstruction for Arbitrary Polyhedra Unstructured Grids

The gradient calculation for the reconstruction of dependent variables is one of the critical issues for the accuracy and robustness of computational fluid dynamics (CFD) methods. If this condition is not satisfied, unphysical new extrema can be generated, leading to the blowup of the flow computation. The geometrical monotonicity condition, which should be satisfied by a gradient calculation method for robustness, is also introduced and discussed. It is shown that only G-G and GLSQ satisfy this condition. It suggests that the gradient computed by the other methods should be used with some slope limiter for robustness even if flows are smooth. A kind of monotonicity condition, which depends only on mesh geometry, has to be satisfied when the robustness of the CFD scheme is considered.