Algebraic Multigrid Based Preconditionners for Oil Reservoir Simulation

Abstract

Algebraic MultiGrid (AMG) methods have become attractive methods when used as preconditioners for Krylov subspace linear solvers.<br>We present here two preconditioning strategies using AMG methods for the solving of large ill conditioned systems arising from the discretization and linearization of fluid mass conservation laws.<br><br>The first strategy is a "combinative" preconditioner combining an ILU(0) step on all types of unknowns(pressure, saturation) and a more specific step on pressure unknowns with an AMG method.<br>The second strategy is performed in a single step with a Block Aggregation AMG. The Block Aggregation AMG method has been developed to cope with matrices araising from the discretization and the linearization of PDE systems. It is also known for its low computational cost and its simple implementation in comparison to classical AMG. This simplicity has to be paid: Aggregation AMG is less efficient than classical AMG, which led us to enhance it with an ILU(0) smoother.<br><br>One difficulty of PDE systems is the coupling existing between the different types of unknowns. A widespread idea, in reservoir simulation, proposes to perform a "local decoupling" by scaling the original matrix of the system by the inverse of the block diagonal matrix built with the diagonal blocs of the original matrix.<br>We will see that the scaling/decoupling of the original system is not well suited for AMG based preconditioners, resulting in bad performances of the linear solver. As a consequence, we will abandon the scaling/decoupling of the original matrix when using an AMG preconditioner.<br><br>The two AMG based preconditioners and a simple ILU(0) preconditioner will be compared on "black oil" simulations on fields with highly heterogeneous permeabilities.