Internal Research Projects
Internal Research Project I-01
In models concerning coupled free-flow and porous-medium flow, the different behavior of the two flow regimes typically results in an unbalanced system of equations. As a result, a fully coupled system often becomes computationally expensive, sometimes even infeasible, to solve in a monolithic manner.
The main objective of this project is to develop and analyse efficient solution methods for coupled free-flow porous-media flow problems based on iterative decoupling strategies, implement the proposed methods numerically in a unified software framework, and extend the approaches to related, more complex flow problems. Two extensions have a central focus within this project, namely the adaptation to multi-rate time stepping and generalizations to non-linear
problems. These non-linear extensions include using the Navier-Stokes equations in the free flow domain and introducing multi-phase flow to the system.
Internal Research Project I-02
Coupling porous media and free-flow is a common denominator of CFD research within SFB 1313, with a multitude of application domains. To address these problems computationally, the ‘coupled until proven uncoupled’ paradigm has been established. One way to achieve full coupling also in a numerical scheme is the monolithic approach, which is particularly attractive if the porous medium is described by some averaged formulation such as Darcy’s Law in the most simple case: All underlying physics, such as variants of the Navier-Stokes equations in the free-flow domain, and Darcy-like equations for the porous medium, are assembled into one nonlinear system. However, it turns out that this system, and linearised variants thereof, are notoriously hard to solve with classical iterative schemes for linear(ised) systems. This is due to the extreme difference in the rate in which the flow in the two domains is evolving, and in the scale difference of the domains of interest. In this auxiliary project, we will primarily examine novel and specifically tailored preconditioning techniques to solve monolithic systems with iterative schemes. In addition, we examine variants of monolithic Newton-like approaches for the nonlinear loop.
Internal Research Project I-03
The development of numerical models for the simulation of flow and transport processes in fractured porous media is an active field of research, given the importance of fractures in a variety of geotechnical engineering applications such as groundwater management, geothermal energy or unconventional gas production techniques. Numerous approaches have been developed which can generally be classified into continuum fracture models and discrete fracture-matrix (dfm) models. While in the first class of models the fractures are accounted for in an averaged sense, the fractures are explicitly captured in dfm models, and are often described by means of lower-dimensional geometries due to their small thicknesses. In recent years, we have developed several dfm models for single-, two-phase, and non-isothermal flow, in which the fractures are described by means of lowerdimensional geometries, and where the flow along them is described on the basis of cross section-average partial differential equations. As a result, a mixeddimensional system of equations describes flow through the fractured porous medium, with transmission conditions for the mass and energy transfer between the fractures and the surrounding bulk medium. We have used several well-established finite-volume schemes for the spatial discretization of the resulting equations, and have studied and compared them in terms of accuracy and computational efficiency by means of numerical analysis.