DuMux 3 – an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling

Authors: Timo Koch and Dennis Gläser and Kilian Weishaupt and Sina Ackermann and Martin Beck and Beatrix Becker and Samuel Burbulla and Holger Class and Edward Coltman and Simon Emmert and Thomas Fetzer and Christoph Grüninger and Katharina Heck and Johannes Hommel and Theresa Kurz and Melanie Lipp and Farid Mohammadi and Samuel Scherrer and Martin Schneider and Gabriele Seitz and Leopold Stadler and Martin Utz and Felix Weinhardt and Bernd Flemisc

A new simulation framework for soil-root interaction, evaporation, root growth, and solute transport

We have developed a general model concept and a flexible software framework for the description of plant-scale soil-root interaction processes including the essential fluid mechanical processes in the vadose zone. The model was developed in the framework of non-isothermal, multiphase, multicomponent flow and transport in porous media. The software is an extension of the open-source porous media flow and transport simulator DuMux to embedded mixed-dimensional coupled schemes. Our coupling concept allows us to describe all processes in a strongly coupled form and adapt the complexity of the governing equations in favor of either accuracy or computational efficiency. We have developed the necessary numerical tools to solve the strongly coupled nonlinear partial differential equation systems that arise with a locally mass conservative numerical scheme even in the context of evolving root architectures. We demonstrate the model concept and its features, discussing a virtual hydraulic lift experiment including evaporation, root tracer uptake on a locally refined grid, the simultaneous simulation of root growth and root water uptake, and an irrigation scenario comparing different models for flow in unsaturated soil. We have analyzed the impact of evaporation from soil on the soil water distribution around a single plant’s root system. Moreover, we have shown that locally refined grids around the root system increase computational efficiency while maintaining accuracy. Finally, we demonstrate that the assumptions behind the Richards equation may be violated under certain conditions

A new simulation framework for soil-root interaction, evaporation, root growth, and solute transport

We have developed a general model concept and a flexible software framework for the description of plant-scale soil-root interaction processes including the essential fluid mechanical processes in the vadose zone. The model was developed in the framework of non-isothermal, multiphase, multicomponent flow and transport in porous media. The software is an extension of the open-source porous media flow and transport simulator DuMux to embedded mixed-dimensional coupled schemes. Our coupling concept allows us to describe all processes in a strongly coupled form and adapt the complexity of the governing equations in favor of either accuracy or computational efficiency. We have developed the necessary numerical tools to solve the strongly coupled nonlinear partial differential equation systems that arise with a locally mass conservative numerical scheme even in the context of evolving root architectures. We demonstrate the model concept and its features, discussing a virtual hydraulic lift experiment including evaporation, root tracer uptake on a locally refined grid, the simultaneous simulation of root growth and root water uptake, and an irrigation scenario comparing different models for flow in unsaturated soil. We have analyzed the impact of evaporation from soil on the soil water distribution around a single plant’s root system. Moreover, we have shown that locally refined grids around the root system increase computational efficiency while maintaining accuracy. Finally, we demonstrate that the assumptions behind the Richards equation may be violated under certain conditions

The Dune framework: Basic concepts and recent developments

This paper presents the basic concepts and the module structure of the Distributed and Unified Numerics Environment and reflects on recent developments and general changes that happened since the release of the first Dune version in 2007 and the main papers describing that state Bastian etal. (2008a, 2008b). This discussion is accompanied with a description of various advanced features, such as coupling of domains and cut cells, grid modifications such as adaptation and moving domains, high order discretizations and node level performance, non-smooth multigrid methods, and multiscale methods. A brief discussion on current and future development directions of the framework concludes the paper

Finite element discretization methods for velocity-pressure and stream function formulations of surface Stokes equations

In this paper we study parametric TraceFEM and parametric SurfaceFEM (SFEM) discretizations of a surface Stokes problem. These methods are applied both to the Stokes problem in velocity-pressure formulation and in stream function formulation. A class of higher order methods is presented in a unified framework. Numerical efficiency aspects of the two formulations are discussed and a systematic comparison of TraceFEM and SFEM is given. A benchmark problem is introduced in which a scalar reference quantity is defined and numerically determined.Comment: 26 page

A Parametric Finite-Element Discretization of the Surface Stokes Equations

We study a higher-order surface finite-element (SFEM) penalty-based discretization of the tangential surface Stokes problem. Several discrete formulations are investigated which are equivalent in the continuous setting. The impact of the choice of discretization of the diffusion term and of the divergence term on numerical accuracy and convergence, as well as on implementation advantages, is discussed. We analyze the inf-sup stability of the discrete scheme in a generic approach by lifting stable finite-element pairs known from the literature. A discretization error analysis in tangential norms then shows optimal order convergence of an isogeometric setting that requires only geometric knowledge of the discrete surface.Comment: 36 pages, 5 figure