Hi all, I am exploring the constraints matrix class with a view to using it to avoid some of the difficulties arising from a problem with strong fluid-structure interaction. The fluid model that I am currently using is incompressible Navier-Stokes without body force, advective or viscous terms. (i.e. just dv/dt = - grad (p) and continuity equation). I realize that it is common to combine these equations and solve a Laplacian equation on a scalar field but I am trying a different approach at the moment where I keep the equations separate and solve in the vector space with pressure and velocity.
I have tested passing pressure from my fluid to my deformable boundary and velocity back as a Dirichlet boundary condition but find that this leads to instability. In order to correct this I want to provide my fluid solver with more information about the state of the boundary. Currently the fluid responds to the velocity with a pressure, but I want the solver to 'be aware' of the effect that the pressure will have on the next velocities. To this end I would like to enforce a relationship between the velocity at a node on the boundary and the pressure on that boundary. The relationship would read: velocity = (last velocity) + (projected acceleration due to external forces) + constant * pressure. This relationship is obtained from a simplification of the mechanical boundary condition and applying this expression can hopefully stabilize the system. The expression is of the form: V = k1 + k2 * P. I see that the constraints matrix class can handle linear homogeneous constraints on the degree of freedom. Is it easy to extend this class to handle the case above? Perhaps a way to enforce this type of constraint using the current class would be to add a dummy field to the original P and V fields which is an identity matrix so that it doesn't affect the solver but has k1 enforced as a Dirichlet condition on the dofs required by the constraint. This seems like a hack which avoids implementing a new class but will cause the code to run slower in the long run. I have run into the strong fluid-structure interaction despite a lot of effort to avoid it and I haven't had much experience with these types of problems. If anyone is familiar with these problems and thinks that my idea sounds like a well known approach I would love to know about papers which discuss it. Otherwise if anyone knows of good review papers discussing alternative approaches using the finite element method that would also be much appreciated! Thanks for the help, Michael _______________________________________________ dealii mailing list http://poisson.dealii.org/mailman/listinfo/dealii
