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Poiseuille Flow Cavity Flow Poisson I Poisson II

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Version 1.7: Example Applications

Poiseuille Flow from Navier-Stokes

This code first solves the tubular Poiseulle flow problem in a, at present, straight tube. The solution from the classic CFD computation is then used for initialization of a simulation of the interaction of the simulated blood and the wall that is modelled as linear elastic. The FSI simulation at the moment uses a monolithic predictor-multi-corrector method that is essentially apt to work for most purposes, but comes with high computational costs. Hence it is no longer really pursued, in favor of experiments with weak coupling, and the substructure strong coupling method.
There is no mesh advection, except the interface that is moved in a Lagrangian fashion. For the structure a classic Lagrangian point-of-view is adopted, for the fluid the typical Eulerian description.
Poiseuille1 Poiseuille2

Lid-Driven Cavity

This package provides a flowsolver module for Animath along with the classic lid-driven cavity test case.
The SURC solvers are global-timestep, consistent mass-matrix CFD solvers whose formulation is based on the Charactersitic-Based split method, which is mostly the work of O.C. Zienkievicz and P. Nithiarasu.
The SURC solvers are not yet adapted to problems with inhomogenous pressure boundary conditions. The work is still heavily in progress, so please do not consider this production code.
The local time-step/compressibility experiments failed, likely due to the stronger coupling between the elements with higher spatial accuracy. The local time-stepping that is often used with CBS and linear interpolation, is hence no option.
The SURC4 and SURC6 solvers use an implicit pressure solution, and both converge slowly, but very steadily after a short start-up phase. The SURC5 solver uses pseudo-compressibility and is due to the absence of the pressure split matrix or a simultaneous pressure solution, apt to be the most performant choice for FSI. The down-side of this method is less steady convergence. The most recent version, SURC 7, adds adaptive timesteps to the SURC 6 scheme.
All methods produce the same velocity profiles.

Please note that higher velocities require higher mesh resolutions for stability. E.g. for 1000 a resolution of 8 or higher is recommendable.

cavity B/W 1cavity B/W 4
cavity B/W 1

Flow-direction-indicating particles released from the driving wall. Twice rendered without color and below with coloring and blending turned on.

Poisson on a Cylinder

This example program is designed for verification of the quadratic interpolation. To this end the domain on which the Poisson problem is solved, is chosen to be circular, i.e. a cylinder. The relative error of the numerical solution is written to a file together the mesh resolution.
Computation with curved elements Computation with straight elements

Poisson Equation

This is the most basic test that is applied to a new version of the code. The Poisson equation is a classic static test case for verification of the basic functioning of the matrix and load vector generators and the boundary condition code.
It is configured for use with a version of Animath that uses Sparse Lib/IML++ as iterative matrix solver.

The approach is that both compressibility and the size of the timesteps are made dependent on the relative difference. Such that great changes of velocity between two consecutive timesteps, increase medium compressibility and decrease the size of the next step. The results are comparative to reference data of Chorin already at low mesh resolutions.