A one-dimensional local discontinuous Galerkin Richards’ equation solution with dual-time stepping
A one-dimensional local discontinuous Galerkin Richards’ equation solution with dual-time stepping
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DOI：
10.1007/s10596-021-10098-3
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发表时间：
2021-12
影响因子：
2.5
通讯作者：
Yilong Xiao;E. Kubatko;Colton J. Conroy
中科院分区：
文献类型：
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作者：
Yilong Xiao;E. Kubatko;Colton J. Conroy
在空间上采用局部间断Galerkin有限元方法，在时间上采用双时间步长方法，给出了一个紧凑的高阶Richards方程的求解方法。双时间步长方法将一个暂态问题转化为一个稳态问题，使得能够直接计算剩余项，并以一种分步的方式求解隐式方程，从而保持了方法的紧凑性和易于并行计算。对解析解的验证表明，我们的求解器具有高阶误差收敛，并证明了求解器在低空间分辨率下保持高精度的能力；该方法是稳健的，并且精确地求解数值解，其时间步长比通常要求的低阶隐式格式大得多。我们的解算器的弹性(在非线性收敛方面)被展示在均质和层状土壤的入渗中，对于这种情况，Hydrus-1D解被用作评估两种坡度限制方案的性能的定性参考。
We present a compact, high-order Richards’ equation solver using a local discontinuous Galerkin finite element method in space and a dual-time stepping method in time. Dual-time stepping methods convert a transient problem to a steady state problem, enabling direct evaluation of residual terms and resolve implicit equations in a step-wise manner keeping the method compact and amenable to parallel computing. Verification of our solver against an analytical solution shows high-order error convergence and demonstrates the solvers ability to maintain high accuracy using low spatial resolution; the method is robust and accurately resolves numerical solutions with time steps that are much larger than what is normally required for lower-order implicit schemes. Resilience of our solver (in terms of nonlinear convergence) is demonstrated in ponded infiltration into homogeneous and layered soils, for which HYDRUS-1D solutions are used as qualitative references to gauge performance of two slope limiting schemes.