Numerical Method Of Multi-field Coupling Model In Unsaturated Porous Media

Multi-field coupling is widespread in the field of rock mechanics, water resources development, aspects of water conservancy and hydropower dam projects, coal mining, geotechnical exploration, nuclear fuel and high-level radioactive waste disposal. In this paper, the complex of hot- water- force(THM) three field coupling model are studied, the coupling equation numerical solution were discussed, and the discrete format is derived and numerical analysis.First coupling problems and multi-field coupling model are analyzed. And comparison of several typical coupling model in this paper. Discussed heat, water flow and soil skeleton deformation(THM) three field coupling model. This model is included with 10 unknowns 10 differential equations. With forward, backward difference method for 10 complex discrete coupled equations numerically to obtain the discrete format of the equations. Take one equation for example to discuss the convergence and divergence of its differential equation, then gives the truncation error.After that, in a different case difference scheme of coupled model was numerically analyzed by a variety of methods. Because of the complicated nonlinear equations, discrete equations is very difficult to solve. Ideally, assume that the original water vapor effect is neglected in the model, and the volume fraction of liquid phase and solid phase were constant, the nonlinear equations is reduced into linear equations. In three dimensions, considering the space domain and time domain on the grid node dissection, for solution of the unknown up to tens of thousands of discrete equations, and the corresponding coefficient matrix order is very large. using Arnoldi method and a special triangular matrix decomposition(LD algorithm) are used to solve the equations analysis. In order to avoid possible malignant interrupt when iterative calculation, further using the generalized minimal residual algorithm(GMERS) analysis, and discuss the convergence of the iterative method.Finally, the paper studied the discrete solution of the nonlinear equations. Since it is difficult to give a better initial values, the large nonlinear equations obtained cannot be directly applied. So Newton iterative method is not ideal. The homotopy structure of nonlinear equations in this paper is constructed by using the homotopy algorithm. The upper limit of the number of isolated solution to the system(Bezout number) is calculated. And their homotopy iterative format is given.