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
The effects of corrugation and wing planform （shape and aspect ratio） on the aerodynamic force production of model insect wings in sweeping （rotating after an initial start） motion at Reynolds number 200 and 3500 ...The effects of corrugation and wing planform （shape and aspect ratio） on the aerodynamic force production of model insect wings in sweeping （rotating after an initial start） motion at Reynolds number 200 and 3500 at angle of attack 40℃ are investigated, using the method of computational fluid dynamics. A representative wing corrugation is considered. Wing-shape and aspect ratio （AR） of ten representative insect wings are considered; they are the wings of fruit fly, cranefly, dronefly, hoverfly, ladybird, bumblebee, honeybee, lacewing （forewing）, hawkmoth and dragon- fly （forewing）, respectively （AR of these wings varies greatly, from 2.84 to 5.45）. The following facts are shown. （1） The corrugated and flat-plate wings produce approximately the same aerodynamic forces. This is because for a sweeping wing at large angle of attack, the length scale of the corrugation is much smaller than the size of the separated flow region or the size of the leading edge vortex （LEV）. （2） The variation in wing shape can have considerable effects on the aerodynamic force; but it has only minor effects on the force coefficients when the velocity at r2 （the radius of the second ：moment of wing area） is used as the reference velocity; i.e. the force coefficients are almost unaffected by the variation in wing shape. （3） The effects of AR are remarkably small： whenAR increases from 2.8 to 5.5, the force coefficients vary only slightly; flowfield results show that when AR is relatively large, the part of the LEV on the outer part of the wings sheds during the sweeping motion. As AR is increased, on one hand, the force coefficients will be increased due to the reduction of 3-dimensional flow effects; on the other hand, they will be decreased due to the shedding of part of the LEV; these two effects approximately cancel each other, resulting in only minor change of the force coefficients.展开更多
The aerodynamic forces and flow structure of a model insect wing is studied by solving the Navier-Stokes equations numerically.After an initial start from rest,the wing is made to execute an azimuthal rotation(sweepin...The aerodynamic forces and flow structure of a model insect wing is studied by solving the Navier-Stokes equations numerically.After an initial start from rest,the wing is made to execute an azimuthal rotation(sweeping)at a large angle of attack and constant angular velocity.The Reynolds number(Re)considered in the present note is 480(Re is based on the mean chord length of the wing and the speed at 60% wing length from the wing root).During the constant-speed sweeping motion,the stall is absent and large and approximately constant lift and drag coefficients can be maintained.The mechanism for the absence of the stall or the maintenance of large aerodynamic force coefficients is as follows.Soon after the initial start,a vortex ring,which consists of the leading-edge vortex(LEV),the starting vortex,and the two wing-tip vortices,is formed in the wake of the wing.During the subsequent motion of the wing,a base-to-tip spanwise flow converts the vorticity in the LEV to the wing tip and the LEV keeps an approximately constant strength.This prevents the LEV from shedding.As a result, the size of the vortex ring increases approximately linearly with time,resulting in an approximately constant time rate of the first moment of vorticity,or approximately constant lift and drag coefficients. The variation of the relative velocity along the wing span causes a pressure gradient along the wing- span.The base-to-tip spanwise flow is mainly maintained by the pressure-gradient force.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.
基金The project supported by the National Natural Science Foundation of China(10232010 and 10472008)Ph.D.Student Foundation of Chinese Ministry of Education(20030006022)
文摘The effects of corrugation and wing planform （shape and aspect ratio） on the aerodynamic force production of model insect wings in sweeping （rotating after an initial start） motion at Reynolds number 200 and 3500 at angle of attack 40℃ are investigated, using the method of computational fluid dynamics. A representative wing corrugation is considered. Wing-shape and aspect ratio （AR） of ten representative insect wings are considered; they are the wings of fruit fly, cranefly, dronefly, hoverfly, ladybird, bumblebee, honeybee, lacewing （forewing）, hawkmoth and dragon- fly （forewing）, respectively （AR of these wings varies greatly, from 2.84 to 5.45）. The following facts are shown. （1） The corrugated and flat-plate wings produce approximately the same aerodynamic forces. This is because for a sweeping wing at large angle of attack, the length scale of the corrugation is much smaller than the size of the separated flow region or the size of the leading edge vortex （LEV）. （2） The variation in wing shape can have considerable effects on the aerodynamic force; but it has only minor effects on the force coefficients when the velocity at r2 （the radius of the second ：moment of wing area） is used as the reference velocity; i.e. the force coefficients are almost unaffected by the variation in wing shape. （3） The effects of AR are remarkably small： whenAR increases from 2.8 to 5.5, the force coefficients vary only slightly; flowfield results show that when AR is relatively large, the part of the LEV on the outer part of the wings sheds during the sweeping motion. As AR is increased, on one hand, the force coefficients will be increased due to the reduction of 3-dimensional flow effects; on the other hand, they will be decreased due to the shedding of part of the LEV; these two effects approximately cancel each other, resulting in only minor change of the force coefficients.
基金The project supported by the National Natural Science Foundation of China(10232010)
文摘The aerodynamic forces and flow structure of a model insect wing is studied by solving the Navier-Stokes equations numerically.After an initial start from rest,the wing is made to execute an azimuthal rotation(sweeping)at a large angle of attack and constant angular velocity.The Reynolds number(Re)considered in the present note is 480(Re is based on the mean chord length of the wing and the speed at 60% wing length from the wing root).During the constant-speed sweeping motion,the stall is absent and large and approximately constant lift and drag coefficients can be maintained.The mechanism for the absence of the stall or the maintenance of large aerodynamic force coefficients is as follows.Soon after the initial start,a vortex ring,which consists of the leading-edge vortex(LEV),the starting vortex,and the two wing-tip vortices,is formed in the wake of the wing.During the subsequent motion of the wing,a base-to-tip spanwise flow converts the vorticity in the LEV to the wing tip and the LEV keeps an approximately constant strength.This prevents the LEV from shedding.As a result, the size of the vortex ring increases approximately linearly with time,resulting in an approximately constant time rate of the first moment of vorticity,or approximately constant lift and drag coefficients. The variation of the relative velocity along the wing span causes a pressure gradient along the wing- span.The base-to-tip spanwise flow is mainly maintained by the pressure-gradient force.
