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Conforming Finite-Element Methods for Modeling Convection in an Incompressible Rock Matrix

机译：不可压缩岩石矩阵中对流建模的有限元方法

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Coupled heat transport and fluid flow in porous rocks play a role in many geological phenomena, including the formation of hydrothermal mineral deposits, the productivity of geothermal reservoirs and the reliability of geo-sequestration. Due to the low compressibility of the fluid and rock matrix and the long-time scales the fluid can be treated as incompressible. The solution of the incompressible Darcy flux problem and the advection-dominated heat transport both provide numerically challenging problems typically addressed using methods specialized for the individual equations. In order to avoid the usage of two different meshes and solution approximations for pressure, flux, and temperature we propose to use standard conforming finite-element methods on the same mesh for both problems. The heat transport equation is solved using a linearized finite-element flux corrected transport scheme which introduces minimum artificial diffusion based on the discretized transport problem. The Darcy flux calculation from pressure uses a global post-processing strategy which at the cost of an extra partial differential equation leads to highly accurate flux approximation. In the limit of zero element size the flux is in fact incompressible. We investigate the numerical performance of our proposed method on a test problem using the parallelized modeling environment escript. We also test the approach to simulate convection in geologically relevant scenarios.
机译：多孔岩石中的热传递和流体耦合在许多地质现象中起作用，包括热液矿床的形成，地热油藏的生产力和固存的可靠性。由于流体和岩石基质的可压缩性低以及长期积垢，因此可以将流体视为不可压缩的。不可压缩的达西通量问题的解决方案和对流主导的热传递都提供了数值上具有挑战性的问题，这些问题通常使用专门针对各个方程式的方法来解决。为了避免使用两个不同的网格以及压力，通量和温度的近似解，我们针对两个问题建议在同一网格上使用标准的有限元方法。使用线性化有限元通量校正传输方案求解热传输方程，该方案基于离散传输问题引入最小的人工扩散。通过压力进行的达西通量计算使用全局后处理策略，该策略以额外的偏微分方程为代价，从而导致了高精度的通量近似。在零元素尺寸的限制下，通量实际上是不可压缩的。我们使用并行建模环境脚本来研究提出的方法在测试问题上的数值性能。我们还测试了在地质相关情况下模拟对流的方法。

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