Application of Moving Adaptive Meshes in Hyperbolic Problems of Gas Dynamics

It is well known that if the solution of flow equations has regions of high spatial activity, a standard fixed mesh technique is ineffective, since it should contain a very large number of mesh points. In case of hyperbolic problems of gas dynamics there are domains containing shock waves and contact discontinuities. A moving mesh adaptation algorithm is applied to reduce computational costs in practical modeling. In such an approach the grid nodes are relocated so that to increase mesh concentration in the domains of steep moving fronts, emerging steep layers, pulses and shock waves. One of the adaptive mesh generation techniques is the variational approach based on the theory of har-monic mapping between surfaces and on the mesh cells convexity concept [1]. Approximation of the harmonic functional is build in such a way that its discrete counterpart has an infinite barrier on the boundary of the set of unfolded grids. The infinite barrier prevents the grid cells from degenerating that allows for generating unfolded grids both in any simply connected, including nonconvex, and multiply connected 2D domains. The barrier property is of particular importance in the vicinity of shock waves where the cells are very narrow and maximal aspect ratio attains 50 and larger [2]. When modeling 2D hyperbolic problems with discontinuous so-lution on the moving adaptive mesh it is possible to reduce the errors, caused by shocks smearing over the cells, by many factors of ten and therefore to decrease significantly, by several times [2], the total error throughou