Solution adaptive direct variational grids for fluid flow calculations

In the present study, the discrete variational (DV) grid generation method is used to produce suitable two dimensional grids for solving the inviscid Euler equations for transonic flow past an airfoil. Through the use of a reference grid, the DV method provides excellent control over grid line clustering in the interior of the grid while maintaining smoothly varying grid line distributions. A solution adaptive grid procedure has been developed using the DV approach which re-distributes the existing grid points in order to resolve regions of high flow (solution) gradients. The grid point re-distribution is governed by the principle of equidistribution. The adaption procedure is done by creating an adapted reference grid which is used to drive the grid point re-distribution. Results for transonic flow past an airfoil are presented to demonstrate the feasibility of the DV-reference grid approach.