Application of moving adaptive grids for numerical solution of 2D nonstationary problems in gas dynamics

Abstract

SUMMARYSolution-adaptive grid generation procedure is coupled with the Godunov-type solver of the secondorder accuracy. Dynamically adaptive grids, clustered to singularities, allow to increase the accuracy of numerical solution. The theory of harmonic maps is used as a theoretical framework for grid generation. The problem of constructing harmonic coordinates on the surface of the graph of control function is formulated. The projection of these coordinates onto a physical domain produces an adaptive-harmonic structured grid. A variational grid generator which can be used also in the case of unstructured grids with adaptation to a vector-function is described in detail. The discrete functional has an inÿnite barrier on the boundary of the set of grids with all convex cells and this guarantees unfolded grid generation at every time step. Results of test computations are presented.

New high quality adaptive mesh generator utilized in modelling plasma streamer propagation at atmospheric pressures

“…This procedure is simple and easy to program and also enables one to keep the map harmonic even after long times of numerical integration. The harmonic functional approximation is built in such a way that its discrete counterpart has an infinite barrier on the boundary of the set of unfolded grids [20]. In this way, grid cells are prevented from degenerating by the infinite barrier, thereby allowing the generation of unfolded grids both in any simply connected, including non-convex, and multiply connected 2D domains.…”