An Eulerian-Lagrangian substructuring domain decomposition method for unsteady-state advection-diffusion equations (Q2762697)

Advection-diffusion partial differential equations arise in petroleum reservoir simulation, subsurface contaminant transport and remediation, and many other applications. All these problems have solutions with moving step fronts within some relatively small regions, where important chemistry and physics take place. NEWLINENEWLINENEWLINEThe main goal of this article is to develop an effective and efficient domain decomposition method (ELLAM scheme) for these models. This method can accomodate any combination of Dirichlet, Neumann, or Robin boundary conditions. The ELLAM scheme can be formulated by evaluation the space-time integrals in weak formulation of the mentioned problem along the characteristics. The methods generate accurate and stable solutions even if large time steps are used. NEWLINENEWLINENEWLINESome numerical experiments that show the advantages of the domain decomposition method are included, concerning Gaussian pulse and discontinuous initial conditions where the analytical solution is known and then, the \(L_2\) and \(L_1\) errors are added.