Product Line Demos

Diffpack Kernel


Standard model PDEs

Simple simulators for the standard model PDEs such as the Laplace, Poisson, diffusion, heat and Helmholtz equations.

Figure: The temperature distribution in a thick-walled tube with fixed temperature values at the inner and outer boundary. Axi-symmetric problem solved in Cartesian coordinates.

See the solution of a 3D Poisson equation in VRML 2.0 data format.

1D/2D/3D linear wave equation

An efficient finite element solver for the standard, linear wave equation in a general 1D/2D/3D geometry.

Figure: The amplitude of 3D sound waves in a box.

Click for movie! (977 Kb)

See the 3D solution in VRML 2.0 data format!

Convection-diffusion problems

A finite element solver for a scalar convection-diffusion transport equation.

Click for movie! (549 Kb)

Click for movie! (328 Kb)
Two- and three-phase porous media flow

A finite element and finite difference coupled simulator for solving the system of PDEs describing two- and three-phase flow in an oil reservoir.

Figure: The saturation of water in a two-phase porous flow simulation.

See the two-phase simulation in VRML 2.0 data format! (161 Kb)

Here are two quick-time movies: two-phase flow(3.5 Mb) and three-phase flow (3.7 Mb).

Slide generated surface waves

A finite difference simulator for modeling surface waves generated by moving subwater slides.

Figure: The time history of the wave generated by a moving subwater slide.

Boussinesq equations

A finite element solver for weakly dispersive and nonlinear water waves described by a set of coupled, nonlinear PDEs in 2D (Boussinesq equations).

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Figure: The water surface elevation due to an incoming wave over a sea mountain.

Click for movie! (694 Kb)

Nonlinear 3D water wave equations

The UNDA simulator for fully nonlinear 3D water waves, based on a spline collocation method. This simulator is developed under contract with the five oil companies Conoco, Norsk Hydro, Saga, Statoil and Shell.

Figure: The water surface elevation and pressure on 4 oil platform legs.

Click for movie! (505 Kb)

See the UNDA solution in VRML 2.0 data format! (106 Kb)


Figure: Water surface elevation past a prism.

Click for movie! (186 Kb)

Wave power plant design

The ocean simulator aims at assisting an optimal design and choice of location for a wave power plant. It incorporates realistic bathymetry and coastline and different geometrical layouts of the wave power plant itself.

Click for movie! (383 Kb)

Figure: The pictures show preliminary results from the linear part of the simulation. The complex wave height is computed using Diffpack FEM-routines compiled with NUMtype=Complex. We see how an incident wave from the left propagates through the bay and the collector part of the powerplant. The wave radiates out from the collector outlet to the right with a large amplification of the amplitude.

Incompressible Navier-Stokes

A finite element solver for the incompressible Navier-Stokes equations based on a penalty function formulation.

Figure: The pressure field and velocity vectors in a fluid flow in a curved channel.

2D/3D linear elasticity

A finite element solver for isotropic, linear elasticity (2D plain strain and 3D).

Figure: The von Mises yield stress in an elastic body subject to external forces.

Stochastic ODEs

A general solver for ordinary stochastic differential equations on Markov form. Time series simulation and first exit time simulations are provided.

Figure: The random displacement of an oil platform subject to a random (slow-drift) wave force.

Stochastic groundwater flow

A finite element based solver for stochastic groundwater flow (Monte Carlo simulation and first order perturbation method).

Figure: The figure shows a single realization of a log-normally distributed stochastic permeability field. The mean value and standard deviation of the log-permeability are 0.5, and it has an isotropic exponential correlation function with correlation scales equal to unity. The field is generated using a Markov-based method.

See also this presentation in VRML2.0 data format. (21 Kb)

Solidification of alloys

A finite element based solver for a set of nonlinear, time dependent, partial differential equations modeling solidification of alloys.

Figure: The temperature distribution at a specific time level in a solidification process.

Flow of polymer between two plates

Finite element solution of a coupled system of partial differential equations modeling injection and cool-down of a non-Newtonian fluid between two plates with a thin gap. Applications concern polymer forming.

Figure: The black domains represent solid obstacles in the flow field. Green color indicates the displaced air while the color of the fluid is brown. Adaptive grids are used to control the accuracy around the moving front and the solid obstacles.

Click for movie! (384 Kb)

Electrical activity in the human heart

Diffpack has been used for numerical simulation of the excitation process in the human heart to find better quantitative measurement methods for myocardial infarction and ischemia. The simulator solves an equation system consisting of a reaction-diffusion parabolic differential equation and an elliptic equation governing the potential distribution in the cardiac muscle and surrounding tissues.

Click for movie! (195 Kb)

Click for movie! (2.3Mb)

Figure: The potential distribution in the cardiac muscle at a specific time level.

See also this presentation in VRML2.0 data format. (91 Kb)