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Advanced Numerical Methods in the Mathematical Sciences

Ivan Yotov, University of Pittsburgh
Domain Decomposition and Time-Partitioned Methods for Flow in Fractured Poroelastic Media


We discuss a computational framework for modeling multiphysics systems of coupled flow and mechanics problems. The simulation domain is decomposed into a union of subdomains, each one associated with a physical, mathematical, and numerical model. Physically meaningful interface conditions are imposed on the discrete level via mortar finite elements or Nitsche's coupling. We present applications of the framework to modeling flow in fractured poroelastic media and arterial flows based on Navier Stokes/Stokes/Brinkman flows coupled with the Biot system of poroelasticity. We discuss stability and accuracy of the spatial discretizations and loosely coupled non-iterative time-split formulations. We further study the use of the loosely coupled scheme as a preconditioner for the monolithic scheme and establish a spectral equivalence of the two formulations. A reduced-dimension fracture model will also be discussed.