Monotone Non-Galerkin Algebraic Multigrid Method Applied to Reservoir Simulations

Abstract

Commercial reservoir simulators must be very robust and fast. Moreover, current hardware requires the simulators to scale over multiple number of computing nodes and for a fixed (‘strong scalability’) as well as an increasing problem size per computing node (‘weak scalability’). In most current commercial reservoir simulators, due to the different geological structures and properties of hydrocarbon reservoirs and the use of enhanced oil recovery (EOR) techniques, the governing equations are strongly nonlinear and hard to solve. The Jacobian system is solved by FGMRES preconditioned by the two-level constrained pressure residual (CPR) preconditioner. The driving force of the CPR preconditioner is the solution of the pressure equation. The industry standard for solving the pressure equation is the algebraic multigrid (AMG) solver. AMG is well known for its ‘weak scalability’. However, in these applications, AMG has unfavorable ‘strong’ scalability properties. This degradation in scalability is due to the increased level of inter-processor communication in the algorithm. In this paper, a monotone non-Galerkin AMG (MNG-AMG) method is presented. The aim of the method is to reduce the overall communication in MNG-AMG by enforcing a predefined nonzero pattern and monotonicity property (i.e., M-matrices) on each multigrid level. This paper describes the application of the MNG-AMG method in the context of reservoir simulations. We will compare the parallel scalability of the default solver with the MNG-AMG solver and discuss the optimal values for the MNG-AMG solver for a variety of test cases based on full field reservoir simulations.