当前位置：
X-MOL 学术
›
SIAM J. Sci. Comput.
›
论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Nonlinearly Constrained Pressure Residual (NCPR) Algorithms for Fractured Reservoir Simulation
SIAM Journal on Scientific Computing ( IF 3.1 ) Pub Date : 2024-02-12 , DOI: 10.1137/22m1516294 Haijian Yang 1 , Rui Li 2 , Chao Yang 3
SIAM Journal on Scientific Computing ( IF 3.1 ) Pub Date : 2024-02-12 , DOI: 10.1137/22m1516294 Haijian Yang 1 , Rui Li 2 , Chao Yang 3
Affiliation
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A561-A586, February 2024.
Abstract. The constrained pressure residual (CPR) algorithm is a family of well-known and industry-standard preconditioners for large-scale reservoir simulation. The CPR algorithm is a two-stage preconditioner to deal with different blocks stage-by-stage, and is often able to effectively improve the robustness behavior and the convergence speed of linear iterations. Nonetheless, as a linear preconditioner, it is hard for the traditional CPR method to be capable of action at the nonlinear level for effectively solving large sparse nonlinear systems of equations with high nonlinearity. In this paper, we present and study the extension of this linear method to the nonlinearly CPR (NCPR) case for solving fractured reservoir problems, to deal with the difficulty of the slow convergence or stagnation from the nonlinear level. In the proposed nonlinear preconditioning, a subspace nonlinear block system is first built and solved to remove the unbalanced nonlinearities of the pressure and the saturation fields, and the fast convergence can then be restored when a variant of semismooth Newton methods is called after the subspace nonlinear block system is solved. Experiments on two or three dimensional porous media applications are presented to demonstrate the applicability and parallel scalability of the aforementioned NCPR method. We also show that the proposed algorithm is superior to the commonly used nonlinear algorithm in terms of the robustness and the positivity-preserving property.
更新日期：2024-02-13
Abstract. The constrained pressure residual (CPR) algorithm is a family of well-known and industry-standard preconditioners for large-scale reservoir simulation. The CPR algorithm is a two-stage preconditioner to deal with different blocks stage-by-stage, and is often able to effectively improve the robustness behavior and the convergence speed of linear iterations. Nonetheless, as a linear preconditioner, it is hard for the traditional CPR method to be capable of action at the nonlinear level for effectively solving large sparse nonlinear systems of equations with high nonlinearity. In this paper, we present and study the extension of this linear method to the nonlinearly CPR (NCPR) case for solving fractured reservoir problems, to deal with the difficulty of the slow convergence or stagnation from the nonlinear level. In the proposed nonlinear preconditioning, a subspace nonlinear block system is first built and solved to remove the unbalanced nonlinearities of the pressure and the saturation fields, and the fast convergence can then be restored when a variant of semismooth Newton methods is called after the subspace nonlinear block system is solved. Experiments on two or three dimensional porous media applications are presented to demonstrate the applicability and parallel scalability of the aforementioned NCPR method. We also show that the proposed algorithm is superior to the commonly used nonlinear algorithm in terms of the robustness and the positivity-preserving property.
京公网安备 11010802027423号