Computational technology for improving the quality of difference schemes based on moving nodes

Abstract

In our papers by us [11],[12] a new method of moving nodes (MMN) was introduced to obtain an approximate analytical solution and construct compact schemes for a one-dimensional convective-diffusion problem. It is proposed to improve the scheme in a three-point pattern. As an initial scheme, a counter flow with one-sided differences is taken. In the QUICK scheme [5], quadratic up flow interpolation is used to determine convective flow. Here we use the solution obtained by the upwind scheme based on MMN. In our above works, the improvement in the accuracy of difference schemes was obtained on the basis of using the method of multi point MMN. In this work, it is proposed to improve the accuracy of the constructed difference schemes using the three point MMN. This is achieved using a more accurate solution to the unknown function on the edge of the considered control volume, the algorithm of which is described in detail in this work.

A simple way to solve boundary value problems in technological processes

“…In [3], an improvement in the construction of discrete analogs based on Richardson's extrapolation was studied. Work [4] is devoted to improving difference schemes based on the choice of a profile on the edge of the control volume. In [5], the moving node method was used to solve the problem of flow in a combined region.…”

The method of averaging over a movable liquid control volume for some problems of fluid mechanics

“…Some applied problems, for which the movable node method was applied, are presented in [12]. Based on the choice of the velocity profile on the edge of the control volume, qualitative schemes were obtained in [13].…”