We present version 3 of the open-source simulator for flow and transport processes in porous media DuMu x . DuMu x is based on the modular C++ framework Dune (Distributed and Unified Numerics Environment) and is developed as a research code with a focus on modularity and reusability. We describe recent efforts in improving the transparency and efficiency of the development process and community-building, as well as efforts towards quality assurance and reproducible research. In addition to a major redesign of many simulation components in order to facilitate setting up complex simulations in DuMu x , version 3 introduces a more consistent abstraction of finite volume schemes. Finally, the new framework for multi-domain simulations is described, and three numerical examples demonstrate its flexibility.
In this paper, we are concerned with the simulation of blood flow in microvascular networks and the surrounding tissue. To reduce the computational complexity of this issue, the network structures are modeled by a one-dimensional graph, whose location in space is determined by the centerlines of the three-dimensional vessels. The surrounding tissue is considered as a homogeneous porous medium. Darcy's equation is used to simulate flow in the extra-vascular space, where the mass exchange with the blood vessels is accounted for by means of line source terms. However, this model reduction approach still causes high computational costs, in particular, when larger parts of an organ have to be simulated. This observation motivates the consideration of a further model reduction step. Thereby, we homogenize the fine scale structures of the microvascular networks resulting in a new hybrid approach modeling the fine scale structures as a heterogeneous porous medium and the flow in the larger vessels by one-dimensional flow equations. Both modeling approaches are compared with respect to mass fluxes and averaged pressures. The simulations have been performed on a microvascular network that has been extracted from the cortex of a rat brain.
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