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An improved iteration method for the numerical solution of groundwater flow in unsaturated soils

机译：改进的迭代法求解非饱和土壤中地下水的数值

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摘要

An improved Jacobi iterative method with two-side equilibration (TS-IJIM) is developed to model the process of unsaturated groundwater flow. The exponential model was adopted to linearize the nonlinear Richards equation (RE). Numerical discretization employing the finite difference method (FDM) produces a highly ill-conditioned system of linear equations. The TS-IJIM is proposed to reduce the matrix conditional number. Compared with two-side equilibration alone and the improved Jacobi iterative method alone, the proposed method effectively reduces the matrix conditional number, which is smallest when the resultant matrix has the same norm for each row. The TS-IJIM method is insensitive to the relaxation factor. Compared with the conjugate gradient method with a two-side equilibration algorithm, the TS-IJIM has better convergence in solving the highly ill-conditioned system. The conditional number of the ill-conditioned matrix can be reduced to 1.0 using the proposed TS-IJIM. Numerical results show that the proposed method can reduce the conditional number and improve convergence for solving unsaturated groundwater flow. Results also indicate that the proposed model is highly accurate and efficient in computing steady-state and transient 1D and 2D groundwater flow in unsaturated soils.
机译：提出了一种改进的带有两侧平衡的雅可比迭代法（TS-IJIM），用于模拟非饱和地下水流的过程。采用指数模型对非线性Richards方程（RE）进行线性化。使用有限差分法（FDM）进行数值离散会产生病态严重的线性方程组。提出了TS-IJIM以减少矩阵条件数。与单独的两侧平衡和单独的改进的Jacobi迭代方法相比，该方法有效地减少了矩阵条件数，当条件结果矩阵的每一行具有相同的范数时，该条件数最小。 TS-IJIM方法对松弛因子不敏感。与具有两侧平衡算法的共轭梯度法相比，TS-IJIM在求解高病态系统时具有更好的收敛性。使用提出的TS-IJIM，病态矩阵的条件数可以减少到1.0。数值结果表明，该方法可以减少条件数，提高求解非饱和地下水流的收敛性。结果还表明，该模型在计算非饱和土壤中稳态和瞬态一维和二维地下水流量方面具有很高的准确性和效率。

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