Publications
Mathematical and algorithmic issues in multiphysics coupling
The modeling of fluid/structure interaction is of growing importance in both energy and environmental applications. Because of the inherent complexity, these problems must be simulated on parallel machines in order to achieve high resolution. The purpose of this research was to investigate techniques for coupling flow and geomechanics in porous media that are suitable for parallel computation. In particular, our main objective was to develop an iterative technique which can be as accurate as a fully coupled model but which allows for robust and efficient coupling of existing complex models (software). A parallel linear elastic module was developed which was coupled to a three phase three-component black oil model in IPARS (Integrated Parallel Accurate Reservoir Simulator). An iterative de-coupling technique was introduced at each time step. The resulting nonlinear iteration involved solving for displacements and flow sequentially. Rock compressibility was used in the flow model to account for the effect of deformation on the pore volume. Convergence was achieved when the mass balance for each component satisfied a given tolerance. This approach was validated by comparison with a fully coupled approach implemented in the British PetroledAmoco ACRES simulator. Another objective of this work was to develop an efficient parallel solver for the elasticity equations. A preconditioned conjugate gradient solver was implemented to solve the algebraic system arising from tensor product linear Galerkin approximations for the displacements. Three preconditioners were developed: LSOR (line successive over-relaxation), block Jacobi, and agglomeration multi-grid. The latter approach involved coarsening the 3D system to 2D and using LSOR as a smoother that is followed by applying geometric multi-grid with SOR (successive over-relaxation) as a smoother. Preliminary tests on a 64-node Beowulf cluster at CSM indicate that the agglomeration multi-grid approach is robust and efficient.