Blood flow through a narrowed carotid artery. Simulation of atherosklerosis. (Simulation by Stefan Wierling)

Solution snapshots of the Cahn-Larché equation on a locally refined UGGrid. C. Gräser, R. Kornhuber, and U. Sack. Numerical simulation of coarsening in binary solder alloys. Comp. Mater. Sci., 93:221–233, 2014 doi

A CutFEM discretization of the EEG forward problem (Nüßing 2018). Simulated with the DUNE based duneuro toolbox.

The geometry is obtained from an MRI scan of a healthy subject, the image is segmented and a level-set description is generated. To avoid problems with creating a geometry-conforming mesh, a CutFEM method is employed which directly uses the level-set information. Using the forward solution given by Dune, the origin of a measured potential distribution at the head surface is estimated. Visualized using Paraview and Blender.

Heterogeneous hip model with multiple coupled 3d and 1d grids. ECMath project A-CH1 Reduced basis methods in orthopedic hip surgery planning (Simulation by Jonathan Youett)

Large deformation contact problem. J. Youett, O. Sander, R. Kornhuber. A globally convergent filter-trust-region method for large deformation contact problems. SIAM J. Sci. Comp., accepted 2018 (Simulation by Jonathan Youett)

Binary image recovery using a phase field approximation on a dynamic grid. BDE.

Results of the same finite element application running on different grids.

Details can be found in:

P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn, R. Kornhuber, M. Ohlberger, O. Sander. A Generic Grid Interface for Parallel and Adaptive Scientific Computing. Part II: Implementation and Tests in DUNE. Computing 82(2-3):121-138, 2008, Preprint.

From left to right the images show:

1. 2D simulation using Dune::Grid::Alberta
2. 3D simulation using Dune::Grid::Alberta
3. 3D simulation using Dune::Grid::ALU3dGrid with cubes
4. 3D simulation using Dune::Grid::ALU3dGrid with simplices
5. Isosurface of a 3D simulation
6. 2D simulation using Dune::Grid::UGGrid with cubes
7. 3D simulation using Dune::Grid::UGGrid with cubes
8. 3D simulation using Dune::Grid::UGGrid with simplices
9. 3D simulation using Dune::Grid::UGGrid with simplices
10. 3D simulation using Dune::Grid::YaspGrid

Parallel-adaptive simulation of the Euler equations of gas dynamics using a stabilized 3rd order discontinuous Galerkin solver. DK.

An unfitted dG cut-cell discretization of laminar flow at the pore-scale (Engwer 2009).

The geometry is obtained from a micro-CT scan. In order to avoid meshing problems we employed a cut-cell based finite element simulation using discontinuous trial functions. Solving the flow-field at the pore-scale yields an effective permeability at the macro-scale.

Level-set based cut-cell reconstructions as used in this simulation are now available in the dune-tpmc module.

Simulation of the water flow field in the soil and the root xylem of a growing white lupin system. For details see Koch et al 2018.

The geometry is obtained from a white lupin root system. The lighter the color the drier the soil. Arrow visualize the water flow field. Visualized using Paraview. The code used in the publication is available here.

DORiE simulation results for infiltration into a small-scale heterogeneous, hill-shaped domain (left), and for evaporation of contaminated water from a domain filled with a coarse and a fine-grained material (right) (Riedel et al. 2020).

Simulation of a five-spot injection scenario with a strongly heterogeneous domain (SPE10 benchmark) using an IMPES formulation on an adaptively refined grid. For details see dumux.