An unconditionally stable artificial compression method for the time‐dependent groundwater‐surface water flows

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Numerical Methods for Partial Differential Equations Pub Date : 2023-04-10 DOI:10.1002/num.23022

Yi Qin, Yang Wang, Yanren Hou, Jian Li

引用次数: 1

Abstract

In this article, we propose a second order, unconditionally stable artificial compression method for the fully evolutionary Stokes/Darcy and Navier‐Stokes/Darcy equations that model the coupling surface and groundwater flows. It uncouples the surface from the groundwater flow by the Crank‐Nicolson Leapfrog scheme for the discretization in time, and through the artificial compression method without artificial pressure boundary conditions to decouple the velocity and pressure of the incompressible flow. Finally, we have verified the stability and second‐order convergence of the algorithm from theoretical analysis and numerical experiments.

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地下水-地表水流随时间变化的无条件稳定人工压缩方法

在这篇文章中，我们提出了一种二阶、无条件稳定的人工压缩方法，用于完全演化的Stokes/Darcy和Navier‐Stokes/达西方程，该方程模拟了地表和地下水的耦合流动。它通过Crank‐Nicolson Leapfrog格式将地表与地下水流解耦，以便及时离散化，并通过没有人工压力边界条件的人工压缩方法将不可压缩流的速度和压力解耦。最后，我们通过理论分析和数值实验验证了算法的稳定性和二阶收敛性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Methods for Partial Differential Equations 数学-应用数学

CiteScore

7.20

自引率

2.60%

发文量

审稿时长

9 months

期刊介绍： An international journal that aims to cover research into the development and analysis of new methods for the numerical solution of partial differential equations, it is intended that it be readily readable by and directed to a broad spectrum of researchers into numerical methods for partial differential equations throughout science and engineering. The numerical methods and techniques themselves are emphasized rather than the specific applications. The Journal seeks to be interdisciplinary, while retaining the common thread of applied numerical analysis.