Contents
 Standard model PDEs
 1D/2D/3D linear wave equation
 Convectiondiffusion problems
 Two and threephase porous media flow
 Slide generated surface waves
 Boussinesq equations
 Nonlinear 3D water wave equations
 Wave power plant design
 Incompressible NavierStokes
 2D/3D linear elasticity
 Stochastic ODEs
 Stochastic groundwater flow
 Solidification of alloys
 Flow of polymer between two plates
 Electrical activity in the human heart
Simple simulators for the standard model PDEs such as the Laplace, Poisson, diffusion, heat and Helmholtz equations. Figure: The temperature distribution in a thickwalled tube with fixed temperature values at the inner and outer boundary. Axisymmetric problem solved in Cartesian coordinates. See the solution of a 3D Poisson equation in VRML 2.0 data format. 
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. 
A finite element solver for a scalar convectiondiffusion transport equation.
Click for movie! (549 Kb) 
Click for movie! (328 Kb) 
A finite element and finite difference coupled simulator for solving the system of PDEs describing two and threephase flow in an oil reservoir. Figure: The saturation of water in a twophase porous flow simulation. See the twophase simulation in VRML 2.0 data format! (161 Kb) Here are two quicktime movies: twophase flow(3.5 Mb) and threephase flow (3.7 Mb). 
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. 

A finite element solver for weakly dispersive and nonlinear water waves described by a set of coupled, nonlinear PDEs in 2D (Boussinesq equations). 
Figure: The water surface elevation due to an incoming wave over a sea mountain. 
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. See the UNDA solution in VRML 2.0 data format! (106 Kb) 

Figure: Water surface elevation past a prism. 
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. 

Figure: The pictures show preliminary results from the linear part of the simulation.
The complex wave height is computed using Diffpack FEMroutines compiled with 
A finite element solver for the incompressible NavierStokes equations based on a penalty function formulation. Figure: The pressure field and velocity vectors in a fluid flow in a curved channel. 
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. 
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 (slowdrift) wave force. 
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 lognormally distributed stochastic permeability field. The mean value and standard deviation of the logpermeability are 0.5, and it has an isotropic exponential correlation function with correlation scales equal to unity. The field is generated using a Markovbased method. See also this presentation in VRML2.0 data format. (21 Kb) 
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. 
Finite element solution of a coupled system of partial differential equations modeling injection and cooldown of a nonNewtonian 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. 

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 reactiondiffusion parabolic differential equation and an elliptic equation governing the potential distribution in the cardiac muscle and surrounding tissues. 
Figure: The potential distribution in the cardiac muscle at a specific time level. See also this presentation in VRML2.0 data format. (91 Kb) 