Numerical Methods For Nonlinear Seepage Equations

Flow in porous media is generally followed to linear Darcy law. In the case ofhigh-speed flow, especially low permeability of medium flow, high viscosity fluid flow,and special multi-phase flow, the flow velocity and pressure gradient is no longer a linearrelationship, this flow is called non-linear flow, generally available non-linear differentialequations to describe the nonlinear flow.The first part of this paper describes the development and research status quo ofdomestic and foreign non-linear flow equation and its solution methods. The second partthrough researching a large number of nonlinear flow in the research literatures, summednonlinear flow in various situations, focusing on three types of non-seepage equations.The first equation describes the fluid Seepage Regularities at high speed, and the secondequation describes the interaction of two-dimensional two-phase fluid under theinfluence of Seepage Regularities, the third equation describes the viscous Newtonianfluid Seepage Regularities.Because of the complexity, in the actual,solving the analytical solution is a difficulttask of the nonlinear seepage equation, in most cases it’s even impossible; the equationlinearization will make the solution error is too large; Therefore, in practical engineeringcalculations, commonly use numerical discretization method and finite difference method(FDM) is favored for its ease and flexibility in solving problems. In the third and fourparts of the paper are given two types of equations difference scheme and the numericalsimulation work. In addition, the use of finite element analysis software COMSOLsolving the Navier-Stokes equation, the calculation process and results of the numericalsimulation of more complex flow problem.