Ефективний чисельний метод длярозв’язання рiвняння Рiчардса-Клюта звiдстеженням зони повного насичення

Abstract

The article presents modifications for numerical methods for modeling of mass transfer process in porous medium with full saturated zone tracking. The goal of the article is to increase computational efficiency of finding an approximate solution process using division of the area into the two non-intersecting parts: unsaturated zone and zone with full saturation. Numerical methods for solving the one-dimensional Richards-Klute equation with tracking of the full saturated zone have been developed. The cases of monotonic solution and solution with general properties of Richards-Klute equation were considered. A modification of the full saturated zone tracking process using a doubly connected edge list structure have been developed for two-dimensional case. Efficiency increase estimation is proven for one- and two-dimensional cases using probability distibution for a measure of the full saturated zone. A comparative analysis of the proposed modifications was carried out. The results of numerical experiments coincide with the estimates predicted by theory.