Multilevel Constrained Pressure-Temperature Residual Preconditioners for Large-Scale Non-Isothermal Reservoir Simulation via Restricted Additive Schwarz Algorithms  

作　　者：Mei Zhang Haijian Yang Chao Yang Shuyu Sun 

机构地区：[1]School of Mathematics,Hunan University,Changsha,Hunan,410082,P.R.China [2]Shenzhen Research Institute,Hunan University,Shenzhen,518000,PR China [3]School of Mathematical Sciences,Peking University,Beijing,100871,P.R.China [4]Computational Transport Phenomena Laboratory,Physical Science and Engineering Division,King Abdullah University of Science and Technology,Thuwal,23955-6900,Saudi Arabia

出　　处：《Communications in Computational Physics》2023年第8期837-868,共32页计算物理通讯（英文）

基　　金：supported by the National Natural Science Foundation of China(No.12131002 and No.11971006);Shenzhen Science and Technology Program(No.JCYJ20210324130801003);Guangdong Basic and Applied Basic Research Foundation(No.2022A1515010147);Changsha science and technology bureau(No.kh2301001);The fourth author also greatly thanks for the support from King Abdullah University of Science and Technology(KAUST)through the grants BAS/1/1351-01 and URF/1/4074-01.

摘　　要：The industry-standard constrained pressure residual(CPR)algorithm is often able to effectively improve the robustness behavior and the convergence speed of linear iterations for isothermal reservoir simulation.In this paper,we present and study 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 inverse of matrices are computed under a domain decomposition framework by using the restricted additive Schwarz(RAS)algorithm,to equally deal with the coupled thermalpressure-saturation reservoir system and highly exploit the parallelism of supercomputer platforms.Moreover,we introduce and develop a family of multilevel CPTR preconditioners with suitable coarse grid corrections,to further improve the applicability of this two-stage preconditioner for large-scale computation.Numerical results for strong heterogeneous flow problems show that the new approach can dramatically improve the convergence of linear iterations,and demonstrate the superiority of CPTR over the commonly used RAS preconditioners.The parallel scalability of the non-isothermal reservoir simulator is also studied versus a supercomputer with tens of thousands of processors.

关 键 词：Thermal reservoir simulation porous media PRECONDITIONING restricted additive Schwarz algorithm strong and weak scalability 

分 类 号：O17[理学—数学]