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Adaptive conservative time integration for transport in fractured porous media
Advances in Water Resources ( IF 4.7 ) Pub Date : 2022-05-05 , DOI: 10.1016/j.advwatres.2022.104213
Michael Liem , Stephan Matthai , Patrick Jenny

The time step of an explicit time integration scheme for solving time-dependent hyperbolic partial differential equations in a finite volume method (FVM) framework is restricted by the Courant-Friedrichs-Levy (CFL) criterion. Conventional time stepping integrates all grid cells with the same time step. This causes unnecessary computational costs when wave speeds and/or grid spacing vary considerably throughout the domain, and a few critical cells dictate the global time step, although most cells could be advanced with a much larger time step. Adaptive time stepping overcomes this issue by allowing different local time step sizes for each grid cell. The adaptive conservative time integration (ACTI) scheme is a recently developed adaptive time stepping method which relies on local time steps that are equal to the largest time step divided by powers of two.

This work extends the ACTI scheme to tracer transport in fractured porous media. When fluid velocity within highly permeable fractures is higher than in the rock matrix and local grid refinement is applied around fractures, the CFL restriction would require prohibitively small time steps in the vicinity of fractures. For two-dimensional discrete fracture and matrix models of fracture patterns we demonstrate that ACTI reduces the computational cost by orders of magnitude compared to global time stepping while retaining solution accuracy. Empirically, we show that ACTI is stable in combination with a first-order explicit flux discretization scheme. Since combination with a standard higher-order MUSCL scheme can lead to spurious oscillations in the solution, we propose a modified MUSCL scheme relying on advection of an inclined reconstruction (MUSCL-AIR).



中文翻译:

裂缝多孔介质输运的自适应保守时间积分

在有限体积法 (FVM) 框架中求解时间相关双曲偏微分方程的显式时间积分方案的时间步长受到 Courant-Friedrichs-Levy (CFL) 准则的限制。传统的时间步长将所有网格单元与相同的时间步长集成。当波速和/或网格间距在整个域中变化很大时,这会导致不必要的计算成本,并且一些关键单元决定全局时间步长,尽管大多数单元格可以用更大的时间步长前进。自适应时间步长通过为每个网格单元允许不同的本地时间步长来克服这个问题。

这项工作将 ACTI 方案扩展到裂缝多孔介质中的示踪剂传输。当高渗透性裂缝中的流体速度高于岩石基质中的流体速度并且在裂缝周围应用局部网格细化时,CFL 限制将在裂缝附近需要非常小的时间步长。对于二维离散裂缝和裂缝模式的矩阵模型,我们证明与全局时间步长相比,ACTI 将计算成本降低了几个数量级,同时保持了解决方案的准确性。根据经验,我们表明 ACTI 与一阶显式通量离散化方案相结合是稳定的。由于与标准的高阶 MUSCL 方案相结合会导致解决方案中出现虚假振荡,

更新日期:2022-05-06
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