Direct numerical simulations of particulate flows using a finite element/fictitious domain approach

This thesis presents a new finite element method based on a Lagrange multiplier/fictitious domain approach for direct simulation of three dimensional multiphase flow problems involving Navier-Stokes equations coupled with rigid body equations. The basic idea of this new approach is to consider a fluid and particle velocity fields that are defined in the entire domain of interest. The particle field is restricted to be equal to zero outside the particles (an L2 field) and the fluid field is defined everywhere in the domain, including the particles. The two systems of equations are additionally constrained by the assumption that the two fields are equal in the domain occupied by the particles. This additional linear constraint is imposed using a global (defined in the entire domain) Lagrange multiplier. The physical meaning of this multiplier is of the interaction force between the particles and the fluid. Our implementation uses unstructured finite elements for the spatial discretization. The time discretization is performed using a time-splitting method. This allows for a separate treatment of the generalized Stokes problem, the convection terms, and the rigid body (no-slip) constraint. A collision detection mechanism prevents particles from penetrating each other or the walls. The linear solver used is a preconditioned conjugate gradient. The solver has been successfully parallelized and performance has been explored. The code was validated by comparing the results for a spherical particle in different physical settings to experimental data obtained in our laboratory. For these experiments the motion of steel and nylon spheres was recorded using a high speed camera. The images obtained were then analyzed and position and velocity information was obtained for each case. Results presented include one particle settling under the gravity in a fluid initially at rest, wall effects on the terminal velocity and the interaction between several spherical particles where kissing, drafting and tumbling occurs. Speedups obtained with the parallel code are also shown.