Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor'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
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.
contamination transport, mixed finite volume element, characteristic
mixed volume element, local conservation of mass, second order
estimate in
