Numerical methods for modelling infiltration processes in heterogeneous soils and their interactions with surface flows

模拟异质土壤渗透过程及其与地表流相互作用的数值方法

• 批准号: RGPIN-2022-05220
• 负责人: Beljadid, Abdelaziz
• 金额: $ 1.97万
• 依托单位: University of Ottawa
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=759199
• 关键词: Numerical; methods; modelling; infiltration; processes

The aim of the proposed research program is to develop new numerical methods for modelling infiltration processes in heterogeneous soils and their interactions with surface flows. We will propose robust computational techniques for the simulation of unstable infiltration in heterogeneous soils, develop efficient numerical models for coupled surface-subsurface flows, propose error estimators and develop new space-time techniques to improve the accuracy and efficiency of the proposed numerical models. We will use the new continuum model that we have recently developed which accurately describes the formation of gravity fingers during infiltration in soils. Robust and efficient two-dimensional and three-dimensional numerical approximation methods will be developed for a new generation of multiphase-flow models in porous media known as phase-field models. Phase-field models are based on the fact that the non-homogeneity of the system and the macroscopic interfaces should be considered for computing the energy of the system. The sharp interfaces separating different phases in the system should be replaced by diffusive interfaces by the introduction of a diffusive order parameter or phase-field parameter that varies smoothly over thin thickness regions. The spatiotemporal evolution in these regions can be described by a set of coupled partial differential equations and solved numerically using suitable discretization techniques. The time-evolution of the phase-field parameter is derived from the variational principle by minimizing the free energy expression of the system. High-order accurate discretizations will be developed and a suitable temporal integration will be used to deal with the issues of the instability associated with the sources of stiffness in the numerical solutions. The flux terms of the governing equations of the coupled system of surface-subsurface flows can be split into a hyperbolic part and an elliptic part. Non-oscillatory high-order continuous/discontinuous reconstructions of the solutions will be developed in order to design stable and accurate numerical schemes. A suitable temporal scheme is required to deal with the issues of the instability associated with the sources of stiffness in the numerical solutions of the system. The semi-discrete form of the system can be split into linear stiff terms and residual nonlinear non-stiff terms, and implicit time integration methods will be used for stiff terms and the explicit temporal schemes can be used to integrate non-stiff terms. In our approach, we will use errors estimators, mesh adaptation, and propose new technique to accurately capture the propagation of the wetting fronts. The efficiency, convergence and accuracy of the proposed numerical models will be examined by several numerical tests. The spatial convergence rate of the proposed schemes will be determined numerically and the impact of the semi-implicit approach on the temporal order of these methods will be studied.

提出的研究计划的目的是开发新的数值方法来模拟非均质土壤中的入渗过程及其与地表水流的相互作用。我们将提出强大的计算技术来模拟非均质土壤中的不稳定入渗，开发有效的地表-地下耦合流动的数值模型，提出误差估计器，并开发新的时空技术来提高所提出的数值模型的准确性和效率。我们将使用我们最近开发的新的连续体模型，该模型准确地描述了土壤入渗过程中重力指的形成。对于新一代多孔介质中多相流模型，即相场模型，鲁棒和高效的二维和三维数值近似方法将得到发展。相场模型是基于系统和宏观界面的非均匀性来计算系统能量的。通过引入在薄厚度区域上平滑变化的扩散阶参量或相场参量，将系统中分离不同相的尖锐界面替换为扩散界面。这些区域的时空演变可以用一组耦合的偏微分方程来描述，并使用适当的离散化技术进行数值求解。通过最小化系统的自由能表达式，利用变分原理推导出相场参数的时间演化。将发展高阶精确离散化，并使用适当的时间积分来处理数值解中与刚度源相关的不稳定性问题。地表-地下流耦合系统控制方程的通量项可分为双曲线部分和椭圆部分。为了设计稳定和精确的数值格式，将开发解的非振荡高阶连续/不连续重构。在系统的数值解中，需要一个合适的时间格式来处理与刚度源相关的不稳定性问题。系统的半离散形式可分为线性刚性项和残差非线性非刚性项，对刚性项采用隐式时间积分法，对非刚性项采用显式时间格式积分。在我们的方法中，我们将使用误差估计器，网格自适应，并提出新的技术来准确地捕捉湿锋的传播。所提出的数值模型的效率、收敛性和准确性将通过若干数值试验进行检验。本文将用数值方法确定这些方法的空间收敛速度，并研究半隐式方法对这些方法时间顺序的影响。