IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Space-time domain decomposition methods in mixed formulation for ow and transport problems in porous media

  • Jan. 23, 2017
  • 1:15 p.m.
  • LeConte 312

Abstract

We consider global-in-time, nonoverlapping domain decomposition methods using mixed finite elements to model flow and transport problems in porous media. Two types of methods are studied: one is based on a generalization of the Steklov-Poincaré operator to time-dependent problems and one is based on the Optimized Schwarz Waveform Relaxation (OSWR) method in which more general (Robin or Ventcell) transmission conditions are used to accelerate the convergence of the method. For each method, a space-time interface problem is derived and different time steps can be used in different subdomains.

We first study the pure diffusion problem, then extend the results to the advection-diffusion equation where operator splitting is used to treat the advection and the diffusion differently. We also consider extensions of the two methods to the case in which the interface represents a discrete-fracture in a reduced fracture model for flow in a fractured porous medium. Numerical results in 2D for both academic problems and more realistic prototypes for simulations for the underground storage of nuclear waste are presented.

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