Volume no :22, Issue no: 1, February (2020)

A MIXED VOLUME ELEMENT WITH CHARACTERISTIC MIXED VOLUME ELEMENT FOR CONTAMINATION TRANSPORT PROBLEM

Author's: Yirang Yuan, Changfeng Li, Huailing Song and Tongjun Sun
Pages: [1] - [39]
Received Date: December 14, 2019; Revised December 25, 2019
Submitted by:
DOI: http://dx.doi.org/10.18642/jpamaa_7100122108

Abstract

Nonlinear systems of convection-dominated diffusion equations are used as the mathematical model of contamination transport problem which is an important topic in environmental protection science. An elliptic equation defines the pressure, a convection-diffusion equation expresses the concentration of contamination, and an ordinary differential equation interprets the surface absorption concentration. The transport pressure appears in the equation of the concentration which determines the Darcy velocity and also controls the physical process. The method of conservative mixed volume element is used to solve the flow equation which improves the computational accuracy of Darcy velocity by one order. We use the mixed volume element with the characteristic to approximate the concentration. This method of characteristic not only preserves the strong computational stability at sharp front, but also eliminates numerical dispersion and nonphysical oscillation. In the present scheme, we could adopt a large step without losing accuracy. The diffusion is approximated by the mixed volume element. The concentration and its adjoint vector function are obtained simultaneously, and the locally conservative law is preserved. We derive an optimal second order estimates in by using the theory and technique of a priori estimates of a differential equation. From the numerical examples given in the paper, the method shows its potential to be a powerful tool in solving actual problems.

Keywords

contamination transport, mixed finite volume element, characteristic mixed volume element, local conservation of mass, second order estimate in