Testing the Hypotheses on Improvement of Iterative Methods Convergence in Solving the Gas Dynamics System of Equations with Optimal Selection of Initial Approximation

摘要

The work is devoted to the study of supposed increase in the convergence rate of iterative methods for solving the Navier-Stokes equations depending on selection of the initial approximation. Initial approximation was obtained by numerically integrating the system of gas dynamics equations on a coarse structured curvilinear grid using the finite volume method. Detailed grid consisted of the 10-fold higher number of nodes; and the nodes in the detailed grid generally did not coincide with the nodes in the coarse grid. Results obtained were interpolated onto the detailed grid using the Shepard method (inverse weighted average distance) with a quadratic weight function. Quadratic function in the experiment with known data demonstrated the lowest approximation error. The detailed grid nodes were localized in the cells of a coarse grid using the method of angles summation modified to accelerate the performance. Parameters interpolation in the nodes located on the surface of a body was carried out by pulling nodes of the detailed grid into the wall area of the coarse grid. After interpolating the parameters, calculation was continued on the detailed grid using the same numerical method. Application of the initial approximation from the coarse grid demonstrates an almost 3-fold acceleration of convergence of the numerical solution on a grid condensed by 10 times compared to approximation by the incident flow parameters.