UNSTEADY ADJOINT TO THE CUT-CELL METHOD USING MESH ADAPTATION ON GPU’S
K.D. Samouchos, Stergios Katsanoulis, Kyriakos C. Giannakoglou · 2016
In its first part, this paper presents a cut-cell method for simulating 2D unsteady inviscid flows of compressible fluids in domains with moving boundaries.To solve shape optimization problems, the gradient of the aerodynamic shape optimization with respect to (w.r.t.) the design variables is computed via the continuous adjoint approach.An automatic grid adaptation method based on a quad-tree data structure allows low memory usage for storing geometric data.The no-penetration condition along the surface of the emerged bodies, is implemented using a second-order cut-cell approach.To avoid numerical instabilities during the solution of the flow and adjoint PDEs, very small cut-cells are merged with neighboring active cells to yield the finite-volume where the flow or adjoint equations are integrated.In transonic flow simulations, the Cartesian grid is adapted not only to the solid boundaries but, also, to the evolving flow discontinuities.The refined grid follows the moving solid wall and discontinuities, by means of local refinement and derefinement processes.The paper focuses on the schemes used to interpolate the flow solution fields between successive time-steps, as the grid becomes adapted to the moving geometry.During the solution of the unsteady adjoint PDEs, since the adjoint solver marches backwards in time and the adapted Cartesian grids are continuously changing, care should be taken so as to have full access to the necessary geometric quantities at all cells, even if these did not exist at previous time-steps.Both the primal and adjoint solvers are programmed on GPUs (Graphics Processing Units), using CUDA-C, to reduce the optimization wall-clock time.Results are presented for both the analysis and optimization problems.