基于自适应网格的多孔介质中达西尺度降水-溶解模型的高效近似方法

IF 1.7 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Shridhar Kumar, Pratibhamoy Das, Kundan Kumar
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引用次数: 0

摘要

在这项工作中,我们考虑了多孔介质中达西尺度的沉淀-溶解反应输运一维和二维模型,并提供了有效求解这些模型的基于网格的自适应数值近似方法。这些模型由对流-扩散-反应 PDE 组成,反应由 ODE 描述,该 ODE 具有非线性、不连续、可能多值的右侧,用于描述沉淀浓度。水相中的体积浓度会形成前沿,而沉淀浓度则由一个随时间变化的自由移动边界来描述。时间自适应移动网格策略以空间等分布原理为基础,受移动网格 PDE 的支配,在本问题的一维有限差分设置和二维有限元设置中得到了利用和改进。此外,我们还使用了一种基于预测器校正器的算法来求解非线性降水-溶解模型。对于等分布方法,我们选择了自适应监测函数,并根据扩散机制对其进行平滑。通过一维有限差分法和二维有限元法的实例进行了数值测试,以证明所提方法的准确性和高效性。与使用固定网格的数值模拟相比,移动网格细化准确地解析了达西尺度降水-溶解反应输运模型的前沿位置,并降低了计算成本。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Adaptive mesh based efficient approximations for Darcy scale precipitation–dissolution models in porous media

Adaptive mesh based efficient approximations for Darcy scale precipitation–dissolution models in porous media

In this work, we consider the Darcy scale precipitation–dissolution reactive transport 1D and 2D models in a porous medium and provide the adaptive mesh based numerical approximations for solving them efficiently. These models consist of a convection-diffusion-reaction PDE with reactions being described by an ODE having a nonlinear, discontinuous, possibly multi-valued right hand side describing precipitate concentration. The bulk concentration in the aqueous phase develops fronts and the precipitate concentration is described by a free and time-dependent moving boundary. The time adaptive moving mesh strategy, based on equidistribution principle in space and governed by a moving mesh PDE, is utilized and modified in the context of present problem for finite difference set up in 1D and finite element set up in 2D. Moreover, we use a predictor corrector based algorithm to solve the nonlinear precipitation–dissolution models. For equidistribution approach, we choose an adaptive monitor function and smooth it based on a diffusive mechanism. Numerical tests are performed to demonstrate the accuracy and efficiency of the proposed method by examples through finite difference approach for 1D and finite element approach in 2D. The moving mesh refinement accurately resolves the front location of Darcy scale precipitation–dissolution reactive transport model and reduces the computational cost in comparison to numerical simulations using a fixed mesh.

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来源期刊
International Journal for Numerical Methods in Fluids
International Journal for Numerical Methods in Fluids 物理-计算机:跨学科应用
CiteScore
3.70
自引率
5.60%
发文量
111
审稿时长
8 months
期刊介绍: The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction. Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review. The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.
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