NUMERICAL METHOD FOR THREE-DIMENSIONAL NONLINEAR CONVECTION-DOMINATED PROBLEM OF DYNAMICS OF FLUIDS IN POROUS MEDIA

• Published in: Applied mathematics and mechanics Vol. 27; no. 5; pp. 683 - 694
• Main Author: 袁益让 杜宁 王文洽 程爱杰 韩玉笈
• Format: Journal Article
• Language: English
• Published: Institute of Mathematics, Shandong University, Jinan 250100, P. R. China%Physical Exploration Institute of Shengli Petroleum Administration, Dongying 257022, Shandong Province, P. R. China 01.05.2006
• Subjects: Estimates; Fluid flow; Fluids; Mathematical analysis; Mathematical models; Media; Nonlinear dynamics; Operators; 数字模拟; 有限差分法; 流体动力学; 非线性受控对流; upwind fractional steps; nonlinear convection-dominated; dynamics of fluids; convergence; finite difference method; numerical simulation
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-006-0515-1

For the three-dimensional convection-dominated problem of dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Fractional steps techniques are needed to convert a multi-dimensional problem into a series of successive one-dimensional problems. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators, and the theory of prior estimates are adopted. Optimal order estimates are derived to determine the error in the second order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources and predicting the consequences of seawater intrusion and protection projects.