Christian Rivera

A virtual finite element model for centered and eccentric mixer configurations

An implementation of the virtual finite element method with unstructured grids for the modeling of laminar flow in eccentric mixers is presented. The effect of the meshing strategy on the quality of the computed flow field is first carefully investigated with a centered impeller. It is shown that both the number of elements in the vicinity of the impeller and the number of kinematics constraints imposed in the virtual finite element formulation control the computational accuracy. The method is then applied to the case of an eccentric mixer provided with a Rushton turbine showing the capabilities of the proposed approach.

Parallel finite element simulations of incompressible viscous fluid flow by domain decomposition with Lagrange multipliers

A parallel approach to solve three-dimensional viscous incompressible fluid flow problems using discontinuous pressure finite elements and a Lagrange multiplier technique is presented. The strategy is based on non-overlapping domain decomposition methods, and Lagrange multipliers are used to enforce continuity at the boundaries between subdomains. The novelty of the work is the coupled approach for solving the velocity-pressure-Lagrange multiplier algebraic system of the discrete Navier-Stokes equations by a distributed memory parallel ILU (0) preconditioned Krylov method. A penalty function on the interface constraints equations is introduced to avoid the failure of the ILU factorization algorithm. To ensure portability of the code, a message based memory distributed model with MPI is employed. The method has been tested over different benchmark cases such as the lid-driven cavity and pipe flow with unstructured tetrahedral grids. It is found that the partition algorithm and the order of the physical variables are central to parallelization performance. A speed-up in the range of 5-13 is obtained with 16 processors. Finally, the algorithm is tested over an industrial case using up to 128 processors. In considering the literature, the obtained speed-ups on distributed and shared memory computers are found very competitive.