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[Overview]
[Kernel Demo]
[Adaptivity Demo]
[Multilevel Demo]
[Parallel Demo] |
| Diffpack Kernel Demos |
Diffpack Kernel Description| Standard model PDEs |
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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. |
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| 1D/2D/3D linear wave equation |
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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. See the 3D solution in VRML 2.0 data format! (106 Kb) |
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| Convection-diffusion problems |
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A finite element solver for a scalar convection-diffusion transport
equation.
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| Two- and three-phase porous media flow |
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A finite element and finite difference coupled simulator for solving the system of PDEs describing two- and three-phase flow in an oil reservoir.
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). |
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| Slide generated surface waves |
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A finite difference simulator for modeling surface waves generated by
moving subwater slides.
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| Boussinesq equations |
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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.
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| Nonlinear 3D water wave equations |
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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.
![[UNDA]](unda/unda1.gif) Figure: The water surface elevation and pressure on 4 oil platform legs. See the UNDA solution in VRML 2.0 data format! (106 Kb) ![[wave]](xic_wave/xic_wave1.gif) Figure: Water surface elevation past a prism. |
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| Wave power plant design |
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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 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.
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| Incompressible Navier-Stokes |
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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. |
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| 2D/3D linear elasticity |
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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. |
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| Stochastic ODEs |
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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. |
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| Stochastic groundwater flow |
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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) |
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| Solidification of alloys |
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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. |
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| Flow of polymer between two plates |
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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. |
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| Electrical activity in the human heart |
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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) |
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