共查询到20条相似文献,搜索用时 15 毫秒
1.
A new formulation is presented for the modeling of immiscible compressible two-phase flow in porous media taking into account
gravity, capillary effects, and heterogeneity. The formulation is intended for the numerical simulation of multidimensional
flows and is fully equivalent to the original equations, contrary to the one introduced in Chavent and Jaffré (Mathematical
Models and Finite Elements for Reservoir Simulation, 1986). The main feature of this formulation is the introduction of a
global pressure. The resulting equations are written in a fractional flow formulation and lead to a coupled system which consists
of a nonlinear parabolic (the global pressure equation) and a nonlinear diffusion–convection one (the saturation equation)
which can be efficiently solved numerically. A finite volume method is used to solve the global pressure equation and the
saturation equation for the water and gas phase in the context of gas migration through engineered and geological barriers
for a deep repository for radioactive waste. Numerical results for the one-dimensional problem are presented. The accuracy
of the fully equivalent fractional flow model is demonstrated through comparison with the simplified model already developed
in Chavent and Jaffré (Mathematical Models and Finite Elements for Reservoir Simulation, 1986). 相似文献
2.
V. V. Klindukhov 《Mechanics of Solids》2009,44(5):737-743
We consider an axisymmetric contact problem for a transversely isotropic layer on a rigid base. The problem is reduced to
a Fredholm integro-differential equation of the first kind for the contact pressure under the punch. The integral equation
is solved by the collocation method [1]. Some numerical results are presented. 相似文献
3.
A higher resolution edge‐based finite volume method for the simulation of the oil–water displacement in heterogeneous and anisotropic porous media using a modified IMPES method 下载免费PDF全文
Rogério Soares da Silva Paulo Roberto Maciel Lyra Ramiro Brito Willmersdorf Darlan Karlo Elisiário de Carvalho 《国际流体数值方法杂志》2016,82(12):953-978
In this article, we present a higher‐order finite volume method with a ‘Modified Implicit Pressure Explicit Saturation’ (MIMPES) formulation to model the 2D incompressible and immiscible two‐phase flow of oil and water in heterogeneous and anisotropic porous media. We used a median‐dual vertex‐centered finite volume method with an edge‐based data structure to discretize both, the elliptic pressure and the hyperbolic saturation equations. In the classical IMPES approach, first, the pressure equation is solved implicitly from an initial saturation distribution; then, the velocity field is computed explicitly from the pressure field, and finally, the saturation equation is solved explicitly. This saturation field is then used to re‐compute the pressure field, and the process follows until the end of the simulation is reached. Because of the explicit solution of the saturation equation, severe time restrictions are imposed on the simulation. In order to circumvent this problem, an edge‐based implementation of the MIMPES method of Hurtado and co‐workers was developed. In the MIMPES approach, the pressure equation is solved, and the velocity field is computed less frequently than the saturation field, using the fact that, usually, the velocity field varies slowly throughout the simulation. The solution of the pressure equation is performed using a modification of Crumpton's two‐step approach, which was designed to handle material discontinuity properly. The saturation equation is solved explicitly using an edge‐based implementation of a modified second‐order monotonic upstream scheme for conservation laws type method. Some examples are presented in order to validate the proposed formulation. Our results match quite well with others found in literature. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
4.
AMIXEDMETHODFORTHECREEPOFASKINLAYERHuangLi-du(黄立独)WangQin-que(汪勤悫)(ShanghaiUniversity,Shanghai)MakFak-tatArthur(麦福达)(HongKong... 相似文献
5.
Sebastian Geiger Thomas Driesner Christoph A. Heinrich Stephan K. Matthäi 《Transport in Porous Media》2006,63(3):399-434
We present a new finite element – finite volume (FEFV) method combined with a realistic equation of state for NaCl–H2O to model fluid convection driven by temperature and salinity gradients. This method can deal with the nonlinear variations
in fluid properties, separation of a saline fluid into a high-density, high-salinity brine phase and low-density, low-salinity
vapor phase well above the critical point of pure H2O, and geometrically complex geological structures. Similar to the well-known implicit pressure explicit saturation formulation,
this approach decouples the governing equations. We formulate a fluid pressure equation that is solved using an implicit finite
element method. We derive the fluid velocities from the updated pressure field and employ them in a higher-order, mass conserving
finite volume formulation to solve hyperbolic parts of the conservation laws. The parabolic parts are solved by finite element
methods. This FEFV method provides for geometric flexibility and numerical efficiency. The equation of state for NaCl–H2O is valid from 0 to 750°C, 0 to 4000 bar, and 0–100 wt.% NaCl. This allows the simulation of thermohaline convection in high-temperature
and high-pressure environments, such as continental or oceanic hydrothermal systems where phase separation is common. 相似文献
6.
Clint N. Dawson 《国际流体数值方法杂志》1990,11(6):835-847
The immiscible displacement problem in reservoir engineering can be formulated as a system of partial differential equations which includes an elliptic pressure–velocity equation and a degenerate parabolic saturation equation. We apply a sequential numerical scheme to this problem where time splitting is used to solve the saturation equation. In this procedure one approximates advection by a higher-order Godunov method and diffusion by a mixed finite element method. Numerical results for this scheme applied to gas–oil centrifuge experiments are given. 相似文献
7.
An implicit finite volume model in sigma coordinate system is developed to simulate two‐dimensional (2D) vertical free surface flows, deploying a non‐hydrostatic pressure distribution. The algorithm is based on a projection method which solves the complete 2D Navier–Stokes equations in two steps. First the pressure term in the momentum equations is excluded and the resultant advection–diffusion equations are solved. In the second step the continuity and the momentum equation with only the pressure terms are solved to give a block tri‐diagonal system of equation with pressure as the unknown. This system can be solved by a direct matrix solver without iteration. A new implicit treatment of non‐hydrostatic pressure, similar to the lower layers is applied to the top layer which makes the model free of any hydrostatic pressure assumption all through the water column. This treatment enables the model to evaluate both free surface elevation and wave celerity more accurately. A series of numerical tests including free‐surface flows with significant vertical accelerations and nonlinear behaviour in shoaling zone are performed. Comparison between numerical results, analytical solutions and experimental data demonstrates a satisfactory performance. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
8.
In this paper we consider porous media flow without capillary effects. We present a streamline method which includes gravity
effects by operator splitting. The flow equations are treated by an IMPES method, where the pressure equation is solved by
a (standard) finite element method. The saturation equation is solved by utilizing a front tracking method along streamlines
of the pressure field. The effects of gravity are accounted for in a separate correction step. This is the first time streamlines
are combined with gravity for three-dimensional (3D) simulations, and the method proves favourable compared to standard splitting
methods based on fractional steps. By our splitting we can take advantage of very accurate and efficient 1D methods. The ideas
have been implemented and tested in a full field simulator. In that context, both accuracy and CPU efficiency have tested
favourably. 相似文献
9.
王文洽 《应用数学和力学(英文版)》2004,25(2)
IntroductionWeconsiderthefollowingnonlinearBurgers’equation : u t u u x=ε 2 u x2 , 0 0 ,( 1 )withtheinitialandtheboundaryconditions u(x,0 ) =f(x) , 0 相似文献
10.
Theoretical analysis on hydraulic transient resulted by sudden increase of inlet pressure for laminar pipeline flow 总被引:1,自引:0,他引:1
Hydraulic transient, which is resulted from sudden increase of inlet pressure for laminar pipeline flow, is studied. The partial differential equation, initial and boundary conditions for transient pressure were constructed, and the theoretical solution was obtained by variable-separation method. The partial differential equation, initial and boundary conditions for flow rate were obtained in accordance with the constraint correlation between flow rate and pressure while the transient flow rate distribution was also solved by variable-separation method. The theoretical solution conforms to numerical solution obtained by method of characteristics (MOC) very well. 相似文献
11.
A new formulation is proposed to describe immiscible compressible two-phase flow in porous media. The main feature of this formulation is the introduction of a global pressure. The resulting equations are written in a fractional flow formulation and lead to a coupled system which consists of a nonlinear parabolic (the global pressure equation) and a nonlinear diffusion–convection one (the saturation equation) which can be efficiently solved numerically. To cite this article: B. Amaziane, M. Jurak, C. R. Mecanique 336 (2008). 相似文献
12.
13.
Based on the principle of virtual work, an updated Lagrangian finite element formulation for the geometrical large deformation analysis of galloping of the iced conductor in an overhead transmission line is developed. In numerical simulation, a three-node isoparametric cable element with three translational and one torsional degrees-of-freedom at each node is used to discretize the transmission line. The nonlinear dynamic system equation is solved with the Newmark time integration method and the Newton-Raphson nonlinear iteration. Numerical examples demonstrate the efficiency of the presented method and the developed finite element program. A new possible galloping mode, which may reflect the saturation phenomenon of a nonlinear dynamic system, is discovered under the condition that the lowest order of vertical natural frequency of the transmission line is approximately two times of the horizontal one. 相似文献
14.
E. J. Avital 《国际流体数值方法杂志》2005,48(9):909-927
A fast cosine transform (FCT) is coupled with a tridiagonal solver for the purpose of solving the Poisson equation on irregular and non‐uniform rectangular staggered grids. This kind of solution is required for the pressure field during the simulation of the incompressible Navier–Stokes equations when using the projection method. A new technique using the FCT–tridiagonal solver is derived for the cases where the boundaries of the flow regime do not coincide with the boundaries of the computational domain and for non‐uniform grids. The technique is based on an iterative procedure where a defect equation is solved in every iteration, followed by a relaxation procedure. The method is investigated analytically and numerically to show that the solution converges as a geometric series. The method is further investigated for the effects of the relative size of the rigid body, the grid stretching, size and aspect ratio. The new solver is incorporated with the direct numerical simulation (DNS) and large eddy simulation (LES) techniques to simulate the flows around a backward‐facing step and a 3D rectangular obstacle, yielding results that qualitatively compare well with known results. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
15.
A numerical method (pressure-correction method using a staggered grid) is coupled to a thermodynamic model for compressible
liquid hydrazine. The method is applied to the venting of liquid hydrazine into space, during which the fluid undergoes a
large pressure drop. Below the saturation pressure vaporisation occurs. This takes place near the outlet and induces variations
of temperature, which may cause solidification and pipe clogging. In order to assess the risk of phase changes, numerical
simulations of the venting line have been performed using a quasi one-dimensional approach. The numerical method can handle
compressible flows of fluids with nonconvex equation of state at the low Mach numbers that occur during hydrazine venting.
A numerical study of the liquid behaviour during strong depressurisation is performed. The method is validated using experimental
data, and allows prediction of pressure evolution and vaporisation location along the pipe.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
16.
A new algorithm, which combines the spectral element method with elastic viscous splitting stress (EVSS) method, has been developed for viscoelastic fluid flows in a planar contraction channel. The system of spectral element approximations to the velocity, pressure, extra stress and the rate of deformation variables is solved by a preconditioned conjugate gradient method based on the Uzawa iteration procedure. The numerical approach is implemented on a planar four‐to‐one contraction channel for a fluid governed by an Oldroyd‐B constitutive equation. The behaviour of the Oldroyd‐B fluids in the contraction channel is investigated with various Weissenberg numbers. It is shown that numerical solutions obtained here agree well with experimental measurements and other numerical predictions. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
17.
Modern lubricants often exhibit shear-thinning due to the presence of high molecular weight polymers as additives. Therefore the influence of such non-Newtonian effects on the performances of lubricating systems must be predicted. The corresponding fluid film flow is governed by a non-linear partial differential equation, which generalizes the classical Reynolds equation. Having prescribed adequate boundary conditions, this equation is solved by a finite element method with optimal control. The problem of the square slider bearing lubricated by the Rabinowitsch fluid is solved in order to test the accuracy of the numerical scheme. The pressure and velocity fields are given and compared with the corresponding ones obtained for the Newtonian fluid. 相似文献
18.
A three‐dimensional, non‐hydrostatic pressure, numerical model with k–ε equations for small amplitude free surface flows is presented. By decomposing the pressure into hydrostatic and non‐hydrostatic parts, the numerical model uses an integrated time step with two fractional steps. In the first fractional step the momentum equations are solved without the non‐hydrostatic pressure term, using Newton's method in conjunction with the generalized minimal residual (GMRES) method so that most terms can be solved implicitly. This method only needs the product of a Jacobian matrix and a vector rather than the Jacobian matrix itself, limiting the amount of storage and significantly decreasing the overall computational time required. In the second step the pressure–Poisson equation is solved iteratively with a preconditioned linear GMRES method. It is shown that preconditioning reduces the central processing unit (CPU) time dramatically. In order to prevent pressure oscillations which may arise in collocated grid arrangements, transformed velocities are defined at cell faces by interpolating velocities at grid nodes. After the new pressure field is obtained, the intermediate velocities, which are calculated from the previous fractional step, are updated. The newly developed model is verified against analytical solutions, published results, and experimental data, with excellent agreement. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
19.
20.
This paper studies the partial differential equation with a small coefficient in the highest-order item. This kind of equation
is also named as boundary layer problem. The Burgers equation and modified Burgers equation are analyzed in this approach.
First, these equations are transferred into the strong nonlinear ones, and then the corresponding strong nonlinear equations
are solved based on the perturbation method. The results from the asymptotic method are comparable with those obtained from
numerical computation.
An erratum to this article is available at . 相似文献