Dr Victor Manuel Calo Associate Professor in Applied Mathematics & Computational Science & Earth Science & Engineering, Co-Director of SRI-Center for Numerical Porous Media
10-11 am Wednesday 18 February, Building 210 Room 104 (Elizabeth Jolley Case Study Room)
In this presentation, we describe two important applications in Computational Geoscience.
1. Multiscale Model Reduction for Flows in Heterogeneous Porous Media: We combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational complexity associated with nonlinear flows in highly-heterogeneous porous media. To solve the nonlinear governing equations, we employ the GMsFEM to represent the solution on a coarse grid with multiscale basis functions and apply proper orthogonal decomposition on a coarse grid. Computing the GMsFEM solution involves calculating the residual and the Jacobian on the fine grid. As such, we use local and global empirical interpolation concepts to circumvent performing these computations on the fine grid. The resulting reduced-order approach enables a significant reduction in the flow problem size while accurately capturing the behaviour of fully-resolved solutions. We use random boundary conditions to construct snapshot vectors to build local basis functions. We show that by using only a few of these randomly generated snapshots, we can adequately approximate dominant modes of the solution space. We consider several numerical examples of nonlinear multiscale partial differential equations that are numerically integrated using fully-implicit time marching schemes to demonstrate the effectiveness of the proposed model reduction approach to speed up simulations of nonlinear flows in high-contrast porous media.
2. Finite Element Analysis of Lithospheric Deformation: We describe an efficient and flexible unstructured finite element discretization, which uses linear elements on simplexes that avoids locking. The anti-volumetric locking technique calculates the volumetric strain from the actual volume change of each element instead of from strain rate accumulation. We extend the original finite-difference-based FLAC (Fast Lagrangian Analysis of Continua) algorithm to a finite element formulation with the anti-volumetric locking modification. We demonstrate the capability of the discretization modelling spontaneous formation of normal faults by the reduction of cohesion in a frictional and cohesive elastoplastic layer.
See Flyer here: Victor Calo – Flyer
