Research in the Matuttis Group

Computational fluid dynamics and granular particles in fluids fluid

Movies by Jan Mueller, Deren Pawel, Yuki Nakamura and Jeewan Dewanto.

The main focus or our research is on particles in fluids: While the computation of flow around a fixed obstacle is a rather traditional research field, much less research activity is dedicated to particles which can move with the flow. This includes phenomena from flow to sandstorms, from beach erosion to liquefaction during earthquakes.

We simulate the "full" flow field with the finite element method and the particles with non-slip boundary conditions on the surface with polygons. We use our own code, written in MATLAB. Because the variation of the flow field is very abrupt between the particles, so that the curvature of the velocity field varies continuously, we need element functions which are effectively of third order (Second order elements with "bubble").

With polygonal particles, we can create a pore space which can be exactly discretized with a Delaunay triangulation of the grid. In every time-step where the particle moves, the grid is adjusted to the new particle positions as in the movie to the right.

On the left, we have a simulation of a decaying granular step: The wall of four fixed particles on the right side of the heap is released and the step collapses in a mini-landslide.

It would be a waste of computer time and memory to use a high resolution (small FEM-triangles) in regions where the flow field has only a small variation, like on the right of the collapsing granular step.

The finite-element equations are then solved for the new mesh, and the flow field is computed as a piecewise polynomial solution which covers the whole domain. Accordingly, we can also draw the interpolated flow field with a resolution below the actual triangle sizes.

One can see how a vortex forms around the region where the upper right corner of the step had been.

And this is how it looks with a larger system, i.e. more particles. Parameters are the densities of water and stone, with particle diameter of about 1.4 mm.

The finite element method allows also to compute more complicated flow patterns. In the simulation below, a sand heap under water (with a sealing, so effectively in a pipe) is simulated. It can be seed on the right behind the heap that not only the conventional convection roll behind obstacle forms, but also a "Moffat eddy" on the ceiling forms. Actually, the movie shows only about a third of the system, as a considerable outflow region is necessary in simulations with complicated flow patterns so that vortices bouncing into the outflow boundary do not affect the flow field in the region of interest.

Below, we have a particle which is suspended in flow which pumps into the interstice between two fixed particles. This corresponds to the fluid dynamics of particles clogging a filter, or bacteria transport in soils. The difficulty is not only to get a suitable flow simulation working, but the particle dynamics must be so that there is no ricocheting of the particle in such a way that the flow field does not spike towards unphysical pressure values.

The following movie shows a whole group of particles drifting through a porous soil matrix, with collisions and sticking:

Last edited: July 12 2026 Hans-Georg Matuttis

The main focus or our research is on particles in fluids: While the computation of flow around a fixed obstacle is a rather traditional research field, much less research activity is dedicated to particles which can move with the flow. This includes phenomena from flow to sandstorms, from beach erosion to liquefaction during earthquakes. We simulate the "full" flow field with the finite element method and the particles with non-slip boundary conditions on the surface with polygons. We use our own code, written in MATLAB. Because the variation of the flow field is very abrupt between the particles, so that the curvature of the velocity field varies continuously, we need element functions which are effectively of third order (Second order elements with "bubble").
	With polygonal particles, we can create a pore space which can be exactly discretized with a Delaunay triangulation of the grid. In every time-step where the particle moves, the grid is adjusted to the new particle positions as in the movie to the right. On the left, we have a simulation of a decaying granular step: The wall of four fixed particles on the right side of the heap is released and the step collapses in a mini-landslide. It would be a waste of computer time and memory to use a high resolution (small FEM-triangles) in regions where the flow field has only a small variation, like on the right of the collapsing granular step. The finite-element equations are then solved for the new mesh, and the flow field is computed as a piecewise polynomial solution which covers the whole domain. Accordingly, we can also draw the interpolated flow field with a resolution below the actual triangle sizes. One can see how a vortex forms around the region where the upper right corner of the step had been.
	And this is how it looks with a larger system, i.e. more particles. Parameters are the densities of water and stone, with particle diameter of about 1.4 mm.

The finite element method allows also to compute more complicated flow patterns. In the simulation below, a sand heap under water (with a sealing, so effectively in a pipe) is simulated. It can be seed on the right behind the heap that not only the conventional convection roll behind obstacle forms, but also a "Moffat eddy" on the ceiling forms. Actually, the movie shows only about a third of the system, as a considerable outflow region is necessary in simulations with complicated flow patterns so that vortices bouncing into the outflow boundary do not affect the flow field in the region of interest.

Below, we have a particle which is suspended in flow which pumps into the interstice between two fixed particles. This corresponds to the fluid dynamics of particles clogging a filter, or bacteria transport in soils. The difficulty is not only to get a suitable flow simulation working, but the particle dynamics must be so that there is no ricocheting of the particle in such a way that the flow field does not spike towards unphysical pressure values.

The following movie shows a whole group of particles drifting through a porous soil matrix, with collisions and sticking: