Abstract: Solution-adaptive grid generation procedure is coupled with the Godunov-type solver of the second order 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 meshes with adaptation to a vector-function is described in detail. The discrete functional has an infinite barrier on the boundary of the set of grids with all convex cells and this guarantees unfolded (nondegenerate) grid generation at every time step. Results of test computations are presented. <
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