Modeling of soil dumping based on a modified Upwind Leapfrog difference scheme

Abstract

Abstract The difference scheme is developed for the diffusion-convection problem numerical solution at large grid Peclet numbers. The scheme based on linear combination of the Upwind and Standard Leapfrog difference schemes (LCUSLDS) with weight coefficients obtained by minimizing the approximation error at small Courant numbers. The proposed approach takes into account the function of cell fullness, which allows to increase the accuracy of modeling on the area with complex geometry. The proposed modification of the Upwind Leapfrog difference scheme for the diffusion-convection problem numerical solution has better accuracy compared to other schemes considered in the article for grid values of Peclet numbers in the range 2 ≤ Pe ≤ 20. The problem of substances transport between two coaxial cylinders for large and small values of grid Peclet numbers is considered to test the proposed difference scheme. This movement of the water medium in hydrodynamics is called the Couette-Taylor flow. The steady fluid flow between two infinitely long coaxial circular cylinders is considered.