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01:10 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2010

Shallow water equation with wetting and drying

In this video you can see the movement of a swinging lake, including wetting and drying processes.
  • Published: 2010
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:30 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2010

Flooding

In this video you can see the flooding of the landscape by a "shock wave" on the surface of a river. The underlying mathematical model are the shallow water equations.
  • Published: 2010
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:05 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2010

Burgers equation on a sphere

In this video you can see the numerical solution of a burgers type equation with a fluxfunction, going to the right on the upper hemisphere and to the left on the lower hemissphere. The numerical scheme is a finite volume scheme on a triangular mesh on the sphere.
  • Published: 2010
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
03:58 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg English 2005

Hydrogen-Oxygen detonation

The underlying physical experiment consists of a tube filled with hydrogen and oxygen. Both react and build a detonation front, moving to the right. The mathematical model consists of the compressible Euler equations with reactive source terms. They are solved by a finite volume scheme on an unstructured grid. Next to the detonation front the grid is locally refined and the refinement zone is moving with the front. Different geometries (e.g. with obstacles inside) of the tube are considered.
  • Published: 2005
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: English
02:00 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2010

Two phase flow with phase transition (Navier-Stokes-Kroteweg model)

The underlying physical experiment consists of an ensemble of bubbles of vapor in a fluid. Since they are not in equilibrium they start to move. For the numerical simulation we have used the Navier-Stokes-Korteweg model, which is similar to the compressible Navier-Stokes-equations. The numerical scheme is a discontinuous Galerkin scheme of higher order (up to order 4). The mesh is unstructured and locally refined along the dynamic interfaces.
  • Published: 2010
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:36 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2010

Fluid structure interaction 2

The underlying physical experiment consists of an incompressible flow through an elastic pipe. For the simulation of the flow we use an incompressible Navier-Stokes solver and for the elastic structure a wave type equation on the surface of a cylinder. They are coupled via the pressure on the elastic structure and the timedependent domain for the flow solver.
  • Published: 2010
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:40 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2010

Fluid structure interaction 1

The underlying physical experiment consists of an incompressible flow through an elastic pipe. For the simulation of the flow we use an incompressible Navier-Stokes solver and for the elastic structure a wave type equation on the surface of a cylinder. They are coupled via the pressure on the elastic structure and the timedependent domain for the flow solver.
  • Published: 2010
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
02:43 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2010

Exploding fluxtube

In this video you can see a solution of the time dependent MHD equations corresponding to initial data with a tube-like magnetic field concentration with balanced total pressure and an additional magnetic field tangential to the tube's boundary in a stratified, hydrostatic background atmosphere. The numerical solution is obtained by an explicit finite volume scheme based on one-dimensional approximate Riemann solvers.
  • Published: 2010
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:41 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2003

Transparent (absorbing) boundary conditions for the MHD equations

In this video you can see numerical solutions of the time dependent MHD equations. In the first column on the left you see the solution in a large domain. In order to reduce the numerical cost we want to solve the problem on a smaller domain with suitable boundary conditios on the upper boundary , such that the solution on the smaller domain is close to the solution of the larger domain (first column). In the fourth column (A) we have used absorbing boundary conditions and it turns out that the solution is close to the solution in the larger domain in the first column. In the second (D) and the third column (N) you can see the solutions for Dirichlet and Neumann boundary conditions, respectively. The result is much worse.
  • Published: 2003
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:13 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2011

Tsunami 2

In this video you can see the numerical simulation of a tsunami in the atlantic ocean. The initial data is given by the impact of a meteorite. For the simulation we have used a realistic bottom topography.
  • Published: 2011
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:13 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2005

Numerical schemes for Burgers equations

In this video you can see the numerical solutions of the burgers equation in 1D, obtained by the Friedrichs-scheme, the Lax-Wendroff and a fluxlimiter scheme respectively with respect to Riemann initial data.
  • Published: 2005
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:21 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2010

Forward facing step 2D

The underlying physical experiment is a Mach 3 flow, coming from the left, through a tube with a forward facing step in 2D. In this video you can see the numerical solution of the compressible, timedependent Euler equations in 2D. The numerical scheme is a finite volume scheme on a dynamically, locally refined, irregular mesh.
  • Published: 2010
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:20 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2018

Transport of bubbles in two phase flows

In this movie you see droplets hanging at the top of a container, filled with a fluid with less density. Due to gravity, they are falling down. The Underlying model consists of the incompressible Navier-Stokes equations with jump conditions along the interfaces.
  • Published: 2018
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:24 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2010

Lax-Wendroff scheme

In this video you can see the exact solution (red) and the numerical solution (green) of the burgers equation, obtained by the Lax-Wendroff scheme, with respect to initial data, which are equal to 0.2 and equal to -0.1 for x<0 and x>0 respectively. The grey line shows a numerical solution for a scheme with limiter. The numerical solution (green) of this scheme is strongly oscillating.
  • Published: 2010
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:24 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2010

Engquist-Osher scheme

In this video you can see the exact solution (red) and the numerical solution (green) of the burgers equation, obtained by the Engquist-Osher-scheme, with respect to initial data, which are equal to 0.2 and equal to -0.1 for x<0 and x>0 respectively. The grey line shows a numerical solution for a scheme with limiter.
  • Published: 2010
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:09 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2016

Geometrically induced shocks on moving surfaces

In this video, you see a numerical solution of a nonlinear conservation law on a moving surface. The velocity of the surface is given. The shrinking of the surface is fast, such that an additional geometrically induced shock appears and follows the regular shock.
  • Published: 2016
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:11 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2010

Solution of the Burgers equation on a rotating sphere

In this video you can see the solution of the Burgers equation on a rotating sphere. The corresponding initial data are equal to one on a small circle on the sphere and outside of this circle equal to 0. The typical structure of a shock and a rarefaction wave are shown.
  • Published: 2010
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:09 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2016

Conservation law on a shrinking sphere

In this video, you see a numerical solution of a conservation law on a shrinking sphere. The velocity of the surface is given. In this case the exact solution can be computed.
  • Published: 2016
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:09 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2016

Nonlinear conservation laws on a moving surfaces

In this video, you see a numerical solution of a nonlinear conservation law on a moving surface. The velocity of the surface is given.
  • Published: 2016
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:24 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2010

Godunov scheme for Burgers equation in 1D

In this video you can see the exact solution (red) and the numerical solution (green) of the burgers equation, obtained by the Godunov-scheme, with respect to initial data, which are equal to 0.2 and equal to -0.1 for x<0 and x>0 respectively.
  • Published: 2010
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:13 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2010

Karman vortex street

In this video you can see a flow of an incompressoble fluid in a tube from left to right. In the left part of the tube there is a cylindrical obstacle. Therefore behind the cylinder the flow show a typical flow pattern, the Karman vortex street.
  • Published: 2010
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:12 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2010

Burgers equation on a sphere

In this video you can see the numerical solution of a burgers type equation on a shrinking surface. The velocity of the shrinking process is given and divergence free.
  • Published: 2010
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:15 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2010

Forward facing step 3D

The underying physical experiment is a Mach 3 flow, coming from the left, through a tube with a forward facing step in 3D. In this video you can see the numerical solution of the compressible, timedependent Euler equations in 3D. The numerical scheme is a finite volume scheme on a dynamically, locally refined, irregular mesh. The computation have been done on a parallel computer. One single color indicates the domain for one processor. Due to the timedependent, adaptive grid refinement, the scheme looses its load balancing. After some timesteps the nodes have to be redistributed to obtain again a good load balancing.
  • Published: 2010
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:16 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2010

Dam break in 3D

The underlying physical experiment consists of a lake with a surface on two different levels, which are seperated by a dam. Now we take away the dam and the water from the higher level will flow to the lower level. The results, shown in the movie, are based on a numerical scheme for the shallow water equations.
  • Published: 2010
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:07 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2011

Tsunami 1

In this video you can see the numerical simulation of a tsunami in the atlantic ocean. The initial data is given by the impact of a meteorite. For the simulation we have used a realistic bottom topography.
  • Published: 2011
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
00:24 Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg Silent film 2010

Lax-Friedrichs scheme

In this video you can see the exact solution (red) and the numerical solution (green) of the burgers equation, obtained by the Lax-Friedrichs scheme, with respect to initial data, which are equal to 0.2 and equal to -0.1 for x<0 and x>0 respectively. The grey line shows a numerical solution for a scheme with limiter.
  • Published: 2010
  • Publisher: Kröner, Dietmar, Albert-Ludwigs-Universität Freiburg
  • Language: Silent film
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