饱和-非饱和渗流的数值流形法研究与应用
Saturated-unsaturated seepage by numerical manifold method
-
摘要: 非饱和渗流问题涉及岩土、水利和环境等众多领域,合理有效地模拟非饱和渗流过程具有重要意义。基于数值流形方法(numerical manifold method,NMM)的覆盖思想,建立了非饱和渗流Richards方程的NMM离散格式,相比于有限元方法(finite element method,FEM),NMM的前处理更为灵活,对复杂边界具有更强的适应性。欠松弛技术和集中质量矩阵的引入,有效抑制了求解过程中的数值震荡现象。通过对一维和二维非饱和渗流算例的模拟,验证了算法的有效性与可靠性。Abstract: The unsaturated seepage problem involves many fields, such as geotechnical engineering, hydraulic engineering and environmental engineering. So it is of great significance to simulate the unsaturated flow reasonably and effectively. Based on the cover system of numerical manifold method (NMM), a NMM discrete form is established to solve the Richards equation for the unsaturated flow. Compared with finite element method (FEM), NMM is more flexible in the preprocessing, and more adaptable to complex boundary conditions. By introducing the under-relaxation technique and the lumped mass matrix, the numerical oscillation is eliminated. Through the simulations of 1D and 2D unsaturated seepage problems, the validity and reliability of the proposed algorithm are verified.