Calculation of Gas Oscillations Inside and Outside the Tube-Resonator Using Multilevel Grid

An original scheme for the numerical solution of 2D gas dynamics problems using the Adaptive Mesh Refinement technology is proposed. This scheme uses stationary multilevel grid and multilevel time integration step. The computational domain is divided into a number of sub-regions, for each of which its own regular Cartesian grid with step multiple of two is generated. The second order of accuracy in space and time of the multilevel scheme is provided by quadratic interpolation during synchronization of data for neighboring grids. An original recursive procedure for a multilevel time integration step is proposed. The scheme is tested on an axisymmetric problem of gas dynamics inside and outside an open resonator. The results of numerical experiments for various positions of the boundary between the coarse and fine grids are presented. For each of the regular grids the MacCormack method with time step proportional to the corresponding grid step is used. It is shown that the proposed scheme significantly reduces the number of nodes and operations, saves memory and increases the speed of calculations.