Flow in variably saturated porous media is typically modelled by the Richards equation, a nonlinear elliptic-parabolic equation which is notoriously challenging to solve numerically. In this paper, we propose a robust and fast iterative solver for Richards' equation. The solver relies on an adaptive switching algorithm, based on rigorously derived a posteriori indicators, between two linearization methods: L-scheme and Newton. Although a combined L-scheme/Newton strategy was introduced previously in [List & Radu (2016)], here, for the first time we propose a reliable and robust criteria for switching between these schemes. The performance of the solver, which can be in principle applied to any spatial discretization and linearization methods, is illustrated through several numerical examples.
翻译:在可变饱和的多孔介质中流动通常以理查斯等式为模型,这是一种非线性椭圆极-抛物线等式,在数字上很难解决。在本文中,我们为理查斯等式建议一个强大和快速的迭代解答器。解答器依赖基于严格推算的后继指标的适应性转换算法,两种线性方法之间是:L-scheme和Newton。虽然先前在此处的[List & Radu(List & Radu()] 中引入了一个综合L-scheme/Newton战略,但我们第一次提出了在这两种办法之间转换的可靠和健全的标准。解答器的性能,原则上可以适用于任何空间分解和线性方法,可以通过几个数字示例来说明。