Abstract: Coupled algorithm of using the Godunov's type solver and adaptive moving mesh is considered. In this approach after every mesh iteration the finite-volume flow solver of the second-order accuracy in time and space updates the flow parameters at the new time level directly on the curvilinear moving grid without interpolation from one mesh to another. Method of adaptive grid generation is based on the theory of harmonic maps. Method is variational, i.e. we consider the problem of minimizing a finite-difference function approximating the Dirichlet's functional written for surfaces. The discrete functional has an infinite barrier at the boundary of the set of grids with all convex quadrilateral cells and this guarantees unfolded grid generation during computations both in any simply connected, including nonconvex, and multiply connected 2D domains. When modeling 2D hyperbolic problems with discontinuous solution 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 the overall error.
Key words: Second-order scheme, shock waves, harmonic mapping, moving adaptive mesh, unfolded grid
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