An Eulerian-Lagrangian substructuring domain decomposition method for unsteady-state advection-diffusion equations

We develop an Eulerian-Lagrangian substructuring domain decomposition method for the solution of unsteady-state advection-diffusion transport equations. This method reduces to an Eulerian-Lagrangian scheme within each subdomain and to a type of Dirichlet-Neumann algorithm at subdomain interfaces. The method generates accurate and stable solutions that are free of artifacts even if large time-steps are used in the simulation. Numerical experiments are presented to show the strong potential of the method.