变异Henry问题检验网格Peclet数在数值计算中的重要性

Verifying the importance of mesh Peclet number in numerical simulations using modified Henry problems

有限元法是求解地下水流和溶质运移对流-弥散方程的常用数值方法,它可以精确高效地处理以弥散为主的问题,但求解以对流为主的问题易引起显著的数值振荡。通过Galerkin有限元法对变异Henry问题进行模拟求解,得到了用不同的剖分网格及水动力弥散系数时,在特选节点处的浓度穿透曲线,分析并找到了浓度振荡的原因及合适的消除方法,即若出现浓度数值解在某值附近振荡,可以通过加密网格或增加水动力弥散系数将其消除。模拟结果及其分析表明:即使是研究区域相同,不同的边界条件、不同的水动力弥散系数对网格精度的要求不同;换言之,同一网格对不同模型参数的有效性也不同。网格Peclet数能够有效地判定给定的网格剖分是否会引起浓度振荡,对有限元法数值计算的网格剖分具有指导意义。

Finite element method（ FEM） is one of the most popular numerical methods in solving convectiondiffusion equations of groundwater flow and solute transport problem. It can solve diffusion-dominated problems efficiently,but may induce significant numerical oscillation in convection-dominated problems. In this paper, numerical simulations were conducted using Galerkin FEM to solve modified Henry problems. The breakthrough curves of concentration were plotted at the skillfully-selected observation point for different mesh discretizations and hydrodynamic dispersion coefficients. The reasons for concentration oscillation and suitable methods to eliminate the oscillation were found through theoretical analyses. Namely,the concentration oscillation could be eliminated through mesh refinement or add hydrodynamic dispersion coefficient. Numerical results and analyses indicated that,even if for the same simulation domain,different boundary conditions and hydrodynamic dispersion coefficients may need different meshes in order to obtain accurate numerical solution. Peclet number is efficient in judging numerical oscillation of concentration and can sever as a criterion for mesh discretization in numerical simulations.