Product Line Demos

Adaptivity Toolbox

Contents

 
Advective Transport with Time-Dependent Adaptivity
Advective Transport with Adaptivity

The figures show results from a Diffpack simulator solving an advection problem, utilizing the adapativity toolbox. The same simulator has been used for two different geometries. In both cases, time-dependent adaptivity is utilized by local mesh refinements close to the front of the solution.

Advective Transport with Adaptivity

The lower right picture shows the grid at a given time step of the calculation.


 
An Adaptive Poisson Solver with Corner Singularity
Poisson Problme with Corner Singularity

A classical illustration of the benefits of local mesh refinements is the case of flow around a corner, as depicted here. The different pictures show the different levels of mesh refinement close to the corner, starting with a uniform grid (upper left) and ending with the final grid (lower right).

Poisson Problem with Corner Singularity

This figure shows the magnitude of the velocity field, which grows fast towards the corner (it approaches infinity in the continuous case).


 
2D Porous Media Flow with Adaptivity

The figures below illustrate adaptive meshes generated for exact computations of pressure, saturation and flow of oil and water in an oil reservoir. Particular areas of interest are the input and output bore wells (red and purple cylinders) and the discontinuous properties of the rock material (blue and green areas).

Automatic refinement is based on solution error, yielding high grid density around bore wells and faults. Only a few lines of code were necessary to introduce this type of adaptivity into the original fixed grid simulator.

The figures below depict the pressure, velocity and error fields for this 2D problem.


 
3D Porous Media Flow with Adaptivity

This is identical to the 2D problem except that the simulator is run with the number of spatial dimensions set equal to 3 (this is a run-time choice in the simulator).

Only the grid nodes of the adaptive mesh are shown together with some iso pressure surfaces.

Here is an illustration of the pressure solution in the full volume.