In this paper,an efcient multigrid-DEIM semi-reduced-order model is developed to accelerate the simulation of unsteady single-phase compressible fow in porous media.The cornerstone of the proposed model is that the fu...In this paper,an efcient multigrid-DEIM semi-reduced-order model is developed to accelerate the simulation of unsteady single-phase compressible fow in porous media.The cornerstone of the proposed model is that the full approximate storage multigrid method is used to accelerate the solution of fow equation in original full-order space,and the discrete empirical interpolation method(DEIM)is applied to speed up the solution of Peng-Robinson equation of state in reduced-order subspace.The multigrid-DEIM semi-reduced-order model combines the computation both in full-order space and in reducedorder subspace,which not only preserves good prediction accuracy of full-order model,but also gains dramatic computational acceleration by multigrid and DEIM.Numerical performances including accuracy and acceleration of the proposed model are carefully evaluated by comparing with that of the standard semi-implicit method.In addition,the selection of interpolation points for constructing the low-dimensional subspace for solving the Peng-Robinson equation of state is demonstrated and carried out in detail.Comparison results indicate that the multigrid-DEIM semi-reduced-order model can speed up the simulation substantially at the same time preserve good computational accuracy with negligible errors.The general acceleration is up to 50-60 times faster than that of standard semi-implicit method in two-dimensional simulations,but the average relative errors of numerical results between these two methods only have the order of magnitude 10^(−4)-10^(−6)%.展开更多
We consider the nonlinear difference equations of the form Lu=f（n,u）,n∈Z,where L is a Jacobi operator given by（Lu）（n）=a（n）u（n＋1）＋a（n-1）u（n-1）＋b（n）u（n） for n ∈Z,{a（n）} and {b（n）} are real val...We consider the nonlinear difference equations of the form Lu=f（n,u）,n∈Z,where L is a Jacobi operator given by（Lu）（n）=a（n）u（n＋1）＋a（n-1）u（n-1）＋b（n）u（n） for n ∈Z,{a（n）} and {b（n）} are real valued N-periodic sequences,and f（n,t） is superlinear on t.Inspired by previous work of Pankov[Discrete Contin.Dyn.Syst.,19,419-430（2007）]and Szulkin and Weth[J.Funct.Anal.,257,3802-3822（2009）],we develop a non-Nehari manifold method to find ground state solutions of Nehari-Pankov type under weaker conditions on f.Unlike the Nehari manifold method,the main idea of our approach lies on finding a minimizing Cerami sequence for the energy functional outside the Nehari-Pankov manifold by using the diagonal method.展开更多
基金This study is supported by the National Natural Science Foundation of China(Nos.51904031,51936001)the Beijing Natural Science Foundation(No.3204038)the Jointly Projects of Beijing Natural Science Foundation and Beijing Municipal Education Commission(No.KZ201810017023).
文摘In this paper,an efcient multigrid-DEIM semi-reduced-order model is developed to accelerate the simulation of unsteady single-phase compressible fow in porous media.The cornerstone of the proposed model is that the full approximate storage multigrid method is used to accelerate the solution of fow equation in original full-order space,and the discrete empirical interpolation method(DEIM)is applied to speed up the solution of Peng-Robinson equation of state in reduced-order subspace.The multigrid-DEIM semi-reduced-order model combines the computation both in full-order space and in reducedorder subspace,which not only preserves good prediction accuracy of full-order model,but also gains dramatic computational acceleration by multigrid and DEIM.Numerical performances including accuracy and acceleration of the proposed model are carefully evaluated by comparing with that of the standard semi-implicit method.In addition,the selection of interpolation points for constructing the low-dimensional subspace for solving the Peng-Robinson equation of state is demonstrated and carried out in detail.Comparison results indicate that the multigrid-DEIM semi-reduced-order model can speed up the simulation substantially at the same time preserve good computational accuracy with negligible errors.The general acceleration is up to 50-60 times faster than that of standard semi-implicit method in two-dimensional simulations,but the average relative errors of numerical results between these two methods only have the order of magnitude 10^(−4)-10^(−6)%.
基金Supported by NSFC(Grant No.11571370)the Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20120162110021)of China
文摘We consider the nonlinear difference equations of the form Lu=f（n,u）,n∈Z,where L is a Jacobi operator given by（Lu）（n）=a（n）u（n＋1）＋a（n-1）u（n-1）＋b（n）u（n） for n ∈Z,{a（n）} and {b（n）} are real valued N-periodic sequences,and f（n,t） is superlinear on t.Inspired by previous work of Pankov[Discrete Contin.Dyn.Syst.,19,419-430（2007）]and Szulkin and Weth[J.Funct.Anal.,257,3802-3822（2009）],we develop a non-Nehari manifold method to find ground state solutions of Nehari-Pankov type under weaker conditions on f.Unlike the Nehari manifold method,the main idea of our approach lies on finding a minimizing Cerami sequence for the energy functional outside the Nehari-Pankov manifold by using the diagonal method.
