Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of ...Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local system.Hence,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational costs.Here,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)equations.Numerical experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.展开更多
The processes of flooding—water flooding, polymer flooding and ternary combination flooding—were simulated respectively on a 2-D positive rhythm profile geological model by using the ASP numerical modeling softw...The processes of flooding—water flooding, polymer flooding and ternary combination flooding—were simulated respectively on a 2-D positive rhythm profile geological model by using the ASP numerical modeling software developed by RIPED (Yuan, et al. 1995). The recovery coefficient, remaining oil saturation, sweep efficiency and displacement efficiency were calculated and correlated layer by layer. The results show that the sweep efficiency and displacement efficiency work different effects on different layers in the severely heterogeneous reservoir. The study shows that the displacement efficiency and sweep efficiency play different roles in different layers for severely heterogeneous reservoirs. The displacement efficiency contributes mainly to the high permeability zones, the sweep efficiency to the low permeability zones, both of which contribute to the middle permeable zones. To improve the sweep efficiency in the low permeability zones is of significance for enhancing the whole recovery of the reservoir. It is an important path for improving the effectiveness of chemical flooding in the severely heterogeneous reservoirs to inject ternary combination slug after profile control.展开更多
文摘Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local system.Hence,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational costs.Here,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)equations.Numerical experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.
基金This project is supported by the China National Key Basis Research Project (No: G1999022512)
文摘The processes of flooding—water flooding, polymer flooding and ternary combination flooding—were simulated respectively on a 2-D positive rhythm profile geological model by using the ASP numerical modeling software developed by RIPED (Yuan, et al. 1995). The recovery coefficient, remaining oil saturation, sweep efficiency and displacement efficiency were calculated and correlated layer by layer. The results show that the sweep efficiency and displacement efficiency work different effects on different layers in the severely heterogeneous reservoir. The study shows that the displacement efficiency and sweep efficiency play different roles in different layers for severely heterogeneous reservoirs. The displacement efficiency contributes mainly to the high permeability zones, the sweep efficiency to the low permeability zones, both of which contribute to the middle permeable zones. To improve the sweep efficiency in the low permeability zones is of significance for enhancing the whole recovery of the reservoir. It is an important path for improving the effectiveness of chemical flooding in the severely heterogeneous reservoirs to inject ternary combination slug after profile control.
