## MIXED ELEMENT-CHARACTERISTIC FINITE ELEMENT AND MIXED ELEMENT-CHARACTERISTIC FINITE DIFFERENCE FOR INCOMPRESSIBLE MISCIBLE DARCY-FORCHHEIMER DISPLACEMENT PROBLEM

Published: 2017-05-24

Page: 81-97

YIRANG YUAN *

Institute of Mathematics, Shandong University, Jinan, 250100, P. R. China.

HONGXING RUI

Institute of Mathematics, Shandong University, Jinan, 250100, P. R. China.

CHANGFENG LI

School of Economics, Shandong University, Jinan, 250100, P. R. China.

TONGJUN SUN

Institute of Mathematics, Shandong University, Jinan, 250100, P. R. China.

*Author to whom correspondence should be addressed.

### Abstract

To solve three-dimensional incompressible miscible displacement of Darcy-Forchheimer flow, two different characteristic methods, mixed element-characteristic finite element and mixed elementcharacteristic finite difference, are discussed in the present paper. The flow equation is discretized by the method of mixed element, and the approximation accuracy of Darcy velocity is improved one order. The concentration equation is treated by the characteristic finite element or the characteristic finite difference. The method of characteristics can confirm strong stability of numerical simulation at the fronts, and can avoid numerical dispersion and nonphysical oscillation. A large time step is adopted with small time truncation error, and the whole computation accuracy is improved. Optimal second order estimates in L2 norm are derived by using the theory and special techniques of priori estimates. This study shows the importance and value in theoretical research and application of numerical simulation.

Keywords: Darcy-Forchheimer model, miscible displacement, mixed element-characteristic finite element, mixed element-characteristic finite difference, error estimate

#### How to Cite

YUAN, Y., RUI, H., LI, C., & SUN, T. (2017). MIXED ELEMENT-CHARACTERISTIC FINITE ELEMENT AND MIXED ELEMENT-CHARACTERISTIC FINITE DIFFERENCE FOR INCOMPRESSIBLE MISCIBLE DARCY-FORCHHEIMER DISPLACEMENT PROBLEM. Asian Journal of Mathematics and Computer Research, 18(2), 81–97. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/1034