溶质在固结变形土体中一维运移模型的有限差分解

Finite difference solution of one-dimensional solute transport model in deforming soils

描述溶质在固结变形防渗层中一维运移过程的对流弥散方程是一个变系数二阶偏微分方程,方程中的相关参数是随时空变化的变量,目前只能用数值法求解。采用数值积分法推导出描述溶质在小变形土体中运移的对流弥散方程的有限差分格式,并针对所给的定解问题,用能量法证明差分格式的稳定性。为验证所建差分格式的实用性,将所建差分格式用于求解溶质在不变形土体中的一维运移过程,并将计算结果与解析解进行比较,两者计算结果一致,表明所建差分格式在稳定的前提下是实用的,能够用所建差分格式求解溶质在小变形土体中的运移问题。

The equation describing the transport process of contaminant in a small-strain deformation soil is a second- order partial differential equation, in which the coefficients are variables. By now, it can only be solved by numerical method. A finite difference scheme of the equation was derived by numerical integration method, and the stability of the scheme was proved by using energy method for the established initial-boundary value problem. Finally, the finite difference scheme was used to simulate the transport process of contaminant in rigid soil, and numerical solution and analytical solution were compared. Results show that the numerical solution is consistent with the analytical solution, implying that the established finite difference scheme is practical when it is stable. Hence, the established difference scheme can be used to solve the solute transport problem in a small-strain deformation soil.