Improvement of numerical solution smoothness for the hydrodynamics problems modeling on rectangular grids

Abstract

The article has been devoted to the problem of improvement real numerical modeling accuracy for the viscous fluid flow between two coaxial half-cylinders on rectangular grids taking into account the filling of cells are used to solve this problem. Approximation of the problem with respect to time is performed on the basis of splitting schemes for physical processes. Difference schemes for solving the hydrodynamic problem are proposed. Analytic solution describing the Taylor-Couette flow is used as a standard to evaluate the numerical solution accuracy of hydrodynamics problems. The simulation was performed on a sequence of condensing computed grids of sizes 11 × 21, 21 × 41, 41 × 81, and 81 × 161 nodes for the areas of smooth and piecewise rectangular boundaries. The grids taking into account the filling of cells are used to improve the smoothness of the solution. In the case of piecewise rectangular approximation the numerical solution error reaches 70%. The grids taking into account the filling of cells reduce the numerical solution error to 6% for the test problem. The test problem shows that using the grid condenced in each spatial direction by 8 times does not lead to increasing the accuracy solutions whereas the solutions accuracy obtained on the basis proposed approach has significant advantage in accuracy.