Multilevel Constrained Pressure-Temperature Residual Preconditioners for Large-Scale Non-Isothermal Reservoir Simulation via Restricted Additive Schwarz Algorithms (Communications in Computational Physics, 2023)
The industry-standard constrained pressure residual (CPR) algorithm is often able to effectively improve the robustness behavior and the convergence speedof linear iterations for isothermal reservoir simulation. In this paper, we present andstudy an improved extension of CPR to the constrained pressure-temperature residual(CPTR) version for non-isothermal reservoir problems in heterogeneous porous media. In the proposed preconditioner, the corresponding approximations for the inverseof matrices are computed under a domain decomposition framework by using the restricted additive Schwarz (RAS) algorithm, to equally deal with the coupled thermal-pressure-saturation reservoir system and highly exploit the parallelism of supercomputer platforms. Moreover, we introduce and develop a family of multilevel CPTRpreconditioners with suitable coarse grid corrections, to further improve the applicability of this two-stage preconditioner for large-scale computation. Numerical resultsfor strong heterogeneous flow problems show that the new approach can dramatically improve the convergence of linear iterations, and demonstrate the superiority ofCPTR over the commonly used RAS preconditioners. The parallel scalability of thenon-isothermal reservoir simulator is also studied versus a supercomputer with tensof thousands of processors.
Keywords: Thermal reservoir simulation; porous media; preconditioning; restricted additive Schwarz algorithm; strong and weak scalability.