Numerical solution of Richards’ equation remains challenging to get robust, accurate and cost-effective results, particularly for moving sharp wetting fronts. An adaptive strategy for both space and time is proposed to deal with 2D sharp wetting fronts associated with varying and possibly vanishing diffusivity caused by nonlinearity, heterogeneity and anisotropy. Adaptive time stepping makes nonlinear convergence reliable and backward difference formula provides high-order time scheme. Adaptive mesh refinement tracks wetting fronts with an a posteriori error indicator. The novelty of this paper consists in using this technique in combination with a weighted discontinuous Galerkin framework to better approximate steep wetting fronts by a discontinuity. The potential of the overall approach is shown through various examples including analytical and laboratory benchmarks and simulation of full-scale multi-materials dam wetting experiment.

理查兹方程的数值解决方案仍然难以获得稳健，准确和具有成本效益的结果，特别是对于移动锋利的润湿前沿。提出了一种适用于时间和空间的自适应策略，以处理与非线性，异质性和各向异性引起的扩散性不断变化甚至消失的二维急剧润湿前沿。自适应时间步长使非线性收敛可靠，而后向差分公式提供了高阶时间方案。自适应网格细化通过后验跟踪湿润前沿错误指示器。本文的新颖之处在于将这种技术与加权不连续Galerkin框架结合使用，可以更好地通过不连续性更好地近似陡峭的湿润前沿。通过各种示例，包括分析和实验室基准以及全面的多材料大坝润湿实验的模拟，显示了整体方法的潜力。