A layered algorithm by bidirectional searching is proposed in this paper to solve the problem that it is difficult and time consuming to reach an optimal solution of the route search with multiple parameter restrictio...A layered algorithm by bidirectional searching is proposed in this paper to solve the problem that it is difficult and time consuming to reach an optimal solution of the route search with multiple parameter restrictions for good quality of service. Firstly, a set of reachable paths to each intermediate node from the source node and the sink node based on adjacent matrix transformation are calculated respectively. Then a temporal optimal path is selected by adopting the proposed heuristic method according to a non-linear cost function. When the total number of the accumulated nodes by bidirectional searching reaches n-2, the paths from two directions to an intermediate node should be combined and several paths via different nodes from the source node to the sink node can be obtained, then an optimal path in the whole set of paths can be taken as the output route. Some simulation examples are included to show the effectiveness and efficiency of the proposed method. In addition, the proposed algorithm can be implemented with parallel computation and thus, the new algorithm has better performance in time complexity than other algorithms. Mathematical analysis indicates that the maximum complexity in time, based on parallel computation, is the same as the polynomial complexity of O(kn2-3kn+k), and some simulation results are shown to support this analysis.展开更多
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...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.展开更多
文摘A layered algorithm by bidirectional searching is proposed in this paper to solve the problem that it is difficult and time consuming to reach an optimal solution of the route search with multiple parameter restrictions for good quality of service. Firstly, a set of reachable paths to each intermediate node from the source node and the sink node based on adjacent matrix transformation are calculated respectively. Then a temporal optimal path is selected by adopting the proposed heuristic method according to a non-linear cost function. When the total number of the accumulated nodes by bidirectional searching reaches n-2, the paths from two directions to an intermediate node should be combined and several paths via different nodes from the source node to the sink node can be obtained, then an optimal path in the whole set of paths can be taken as the output route. Some simulation examples are included to show the effectiveness and efficiency of the proposed method. In addition, the proposed algorithm can be implemented with parallel computation and thus, the new algorithm has better performance in time complexity than other algorithms. Mathematical analysis indicates that the maximum complexity in time, based on parallel computation, is the same as the polynomial complexity of O(kn2-3kn+k), and some simulation results are shown to support this analysis.
基金supported by the National Natural Science Foundation of China(No.12131002 and No.11971006)Shenzhen Science and Technology Program(No.JCYJ20210324130801003)+2 种基金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.
文摘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.
