Abstract: Possibility to apply the harmonic mapping using a variational approach in order to generate moving adaptive grids in the hyperbolic problems of gas dynamics is considered. Three-point model of adaptation shows if control/(monitor) function is discontinuous, minimizing the discrete analogy of the harmonic functional it is provided possibility to generate an unfolded mesh with strong grid lines condensing in the vicinity of shocks. The algorithm of redistributing the boundary nodes is suggested consisting in using constrained minimization of the functional when constraints define the boundary of the domain. In real computations due to mesh adaptation it is possible to reduce the errors, caused by shock waves smearing over the cells, by many factors of ten. Modeling of the 2-D supersonic gas flow in the channel has shown to achieve the same accuracy on the adaptive grid with the same structure as the quasiuniform mesh it is required less CPU memory by factor of 25 and running time by factor of 50 to 60. Computational tests of the steady transonic and supersonic flow over an airfoil demonstrate possibility to control mesh sizes across shocks.
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