YUAN Yi-rang, DU Ning, WANG Wen-qia, CHENG Ai-jie, HAN Yu-ji. Numerical Method for the Three-Dimensional Nonlinear Convection-Dominated Problem of Dynamics of Fluids in Porous Media[J]. Applied Mathematics and Mechanics, 2006, 27(5): 605-614.
 Citation: YUAN Yi-rang, DU Ning, WANG Wen-qia, CHENG Ai-jie, HAN Yu-ji. Numerical Method for the Three-Dimensional Nonlinear Convection-Dominated Problem of Dynamics of Fluids in Porous Media[J]. Applied Mathematics and Mechanics, 2006, 27(5): 605-614.

# Numerical Method for the Three-Dimensional Nonlinear Convection-Dominated Problem of Dynamics of Fluids in Porous Media

• Rev Recd Date: 2006-01-18
• Publish Date: 2006-05-15
• 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 were put forward. Fractional steps techniques were 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 were 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.
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