Algorithms for Solving Darcian Flow in Structured Porous Media

Michal Kuráž,Petr Mayer

doi:10.14311/1829

Abstract

This paper presents several algorithms that were implemented in DRUtES [1], a new open source project. DRUtES is a finite element solver for coupled nonlinear parabolic problems, namely the Richards equation with the dual porosity approach (modeling the flow of liquids in a porous medium). Mass balance consistency is crucial in any hydrological balance and contaminant transportation evaluations. An incorrect approximation of the mass term greatly depreciates the results that are obtained. An algorithm for automatic time step selection is presented, as the proper time step length is crucial for achieving accuracy of the Euler time integration method. Various problems arise with poor conditioning of the Richards equation: the computational domain is clustered into subregions separated by a wetting front, and the nonlinear constitutive functions cover a high range of values, while a very simple diagonal preconditioning method greatly improves the matrix properties. The results are presented here, together with an analysis.

Highlights

It is important to be able to predict fluid movement in an unsaturated/saturated zone in many fields, ranging from agriculture, via hydrology, to technical applications of dangerous waste disposal in deep rock formations.The mathematical model of unsaturated flow was originally published by L
This paper has aimed to present several new algorithms that were implemented in the DRUtES opensource project [1] – a finite element solver for nonlinear coupled parabolic problems, namely the Richards equation with the dual porosity approach, in order to improve the accuracy and efficiency of its numerical treatment
The Mass Curve Zone Approach, an efficient and accurate method for the Euler time integration method, has been presented and tested. This method is based on an automatic time step selection

Summary

Introduction

The mathematical model of unsaturated flow was originally published by L. The Richards equation problem has undergone various investigations and numerical treatments. Its finite element solution was originally published by Neuman in 1970 for several engineering applications, e.g. dam seepage modeling, see [3]. A fundamental work analyzing a mass conservation numerical method for the Richards equation was published in 1990 by Celia et al [5].An analysis of the Richards equation problem has been the subject of several works by Kačur, e.g. Various methods for numerical treatment of the problem have recently been published, see e.g. Kees et al [7], Šolín et al [8] or Kuráž et al [9, 10]

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Conclusion