On the solution of fluid flow and solid deformation interaction problems

The objective of this research is to develop numerical methods to solve the coupled field equations of fluid and solid mechanics which arise due to the interaction of fluid flow and solid deformation. Computational methods have been developed for solving a general class of time-dependent incompressible flow problems with solid boundaries that deform under the transient pressure and viscous stresses from the fluid. Three example problems are considered in this work. The first one is a limiting case of fluid solid interaction where the solid is just an elastic membrane enclosing the fluid. A physical counterpart of this is flow involving surface tension. Oscillation of a liquid jet issuing out of an elliptical orifice is chosen as the example problem for this case. The results of solving the Navier-Stokes equations are used to verify the validity of a simplified theoretical model for this physical problem. Two distinct numerical methods are used to solve the N-S equations involving moving boundary conditions. Finite difference method and spectral element methods are used. Both spatial and temporal coordinate transformation is used for the FD formulation of the problem. A Poisson equation for pressure is solved, and hyperbolic-parabolic grid generation is done at each time step. A spectral element method solution to the oscillating jet problem has been obtained. FD solution shows more damping compared to the SEM solution and the solution from the theoretical model, but the period of oscillation of all the three methods agree very closely. The solutions have been numerically validated. The second example problem of fluid flow and solid deformation interaction is the Couette flow with an elastic slab as boundary. A solution method has been demonstrated in which the algebraic equations resulting from the discretization of the fluid and solid equations can be solved separately and still have the solution to the coupled problem. This finding makes the solution of the coupled field equations in higher dimensions more easily implementable on conventional as well as parallel computers. Flow around an elastic cylinder is computed with this methodology, and the results compared with the flow around rigid cylinders.