一类非线性渗流数学模拟

活动边界非线性渗流是现代渗流力学的前沿研究领域之一。在中建立的低渗透介质非线性渗流数学模型为活动边界非线性模型，不能求出其严格解析解，因此分别运用平均质量守恒法、数值模拟法求得了其近似解析解、数值解、二吻合得较好；并得了低渗透介质非线性渗流活动边界的运动规律和压力分布特征。结果表明：起始比降越大，则活动边界发展的速度越小，压力传播越慢。近似解工程意义明确、分析计算简洁，变步长离散数值方法为求解活动边界非线性问题提供了好的工具。

MATHEMATICAL SIMULATION OF NONLINEAR FLOW THROUGH POROUS MEDIA

A nonlinear flow with a moving boundary is one of up-to-date research fields of modern mechanics of fluids in porous media. A mathematical model of a nonlinear flow through low permeability media with a moving boundary is established, an exact analytical solution of the model can not be presented because of the moving boundary. Not only is a numerical solution derived by a finite difference method, but also an approximate analytical solution is given by using an integral method. It is shown that there is good agreement between them. The law of the moving boundary and characteristics of the pressure distribution are derived. Results show that the larger the starting pressure gradient is, the slower the boundary moves, and the slower the pressure transmits. Both approximate analytical solution and numerical simulation can provide engineering design with theoretical basis. The approximate analytical solution has explicit meaning and simplifies analyses and calculation in engineering. The finite difference method that uses variable steps will provide numerical simulation of the three-dimensional nonlinear flow that has a moving boundary with a good method.