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31.
《Numerical Methods for Partial Differential Equations》2018,34(1):228-256
In this article, we will consider the generalized Forchheimer flows for slightly compressible fluids. Using Muskat's and Ward's general form of Forchheimer equations, we describe the fluid dynamics by a nonlinear degenerate parabolic equation for density. The long‐time numerical approximation of the nonlinear degenerate parabolic equation with time dependent boundary conditions is studied. The stability for all time is established in a continuous time scheme and a discrete backward Euler scheme. A Gronwall's inequality‐type is used to study the asymptotic behavior of the solution. Error estimates for the solution are derived for both continuous and discrete time procedures. Numerical experiments confirm the theoretical analysis regarding convergence rates. 相似文献
32.
We study two novel decoupled energy‐law preserving and mass‐conservative numerical schemes for solving the Cahn‐Hilliard‐Darcy system which models two‐phase flow in porous medium or in a Hele–Shaw cell. In the first scheme, the velocity in the Cahn–Hilliard equation is treated explicitly so that the Darcy equation is completely decoupled from the Cahn–Hilliard equation. In the second scheme, an intermediate velocity is used in the Cahn–Hilliard equation which allows for the decoupling. We show that the first scheme preserves a discrete energy law with a time‐step constraint, while the second scheme satisfies an energy law without any constraint and is unconditionally stable. Ample numerical experiments are performed to gauge the efficiency and robustness of our scheme. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 936–954, 2016 相似文献
33.
In the mathematical modelling of compactional flow in porous media, the constitutive relation is typically modelled in terms of a nonlinear relationship between effective pressure and porosity, and compaction is essentially poroelastic. However, at depths deeper than 1 km where the pressure is high, compaction becomes more akin to a viscous one. Two mathematical models of compaction in porous media are formulated and the nonlinear equations are then solved numerically. The essential features of numerical profiles of poroelastic and viscous compaction are thus compared with asymptotic solutions. Two distinguished styles of density-driven compaction in fast and slow compacting sediments are analysed and shown in this paper. 相似文献
34.
35.
Combined, forced, and free flow in a vertical circular duct filled with a porous medium is investigated according to the Darcy–Boussinesq
model. The effect of viscous dissipation is taken into account. It is shown that a thermal boundary condition compatible with
fully developed and axisymmetric flow is either a linearly varying wall temperature in the axial direction or, only in the
case of uniform velocity profile, an axial linear-exponential wall temperature change. The case of a linearly varying wall
temperature corresponds to a uniform wall heat flux and includes the uniform wall temperature as a special case. A general
analytical solution procedure is performed, by expressing the seepage velocity profile as a power series with respect to the
radial coordinate. It is shown that, for a fixed thermal boundary condition, i.e., for a prescribed slope of the wall temperature,
and for a given flow rate, there exist two solutions of the governing balance equations provided that the flow rate is lower
than a maximum value. When the maximum value is reached, the dual solutions coincide. When the flow rate is higher than its
maximum, no axisymmetric solutions exist.
E. Magyari is on leave from the Institute of Building Technology, ETH—Zürich. 相似文献
36.
Most porous solids are inhomogeneous and anisotropic, and the flows of fluids taking place through such porous solids may show features very different from that of flow through a porous medium with constant porosity and permeability. In this short paper we allow for the possibility that the medium is inhomogeneous and that the viscosity and drag are dependent on the pressure (there is considerable experimental evidence to support the fact that the viscosity of a fluid depends on the pressure). We then investigate the flow through a rectangular slab for two different permeability distributions, considering both the generalized Darcy and Brinkman models. We observe that the solutions using the Darcy and Brinkman models could be drastically different or practically identical, depending on the inhomogeneity, that is, the permeability and hence the Darcy number. 相似文献
37.
This paper describes the solution of a steady state natural convection problem in porous media by the dual reciprocity boundary element method (DRBEM). The boundary element method (BEM) for the coupled set of mass, momentum, and energy equations in two dimensions is structured by the fundamental solution of the Laplace equation. The dual reciprocity method is based on augmented scaled thin plate splines. Numerical examples include convergence studies with different mesh size, uniform and non‐uniform mesh arrangement, and constant and linear boundary field discretizations for differentially heated rectangular cavity problems at filtration with Rayleigh numbers of Ra*=25, 50, and 100 and aspect ratios of A=1/2, 1, and 2. The solution is assessed by comparison with reference results of the fine mesh finite volume method (FVM). Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
38.
The problem of the onset of convective roll instabilities in a horizontal porous layer with isothermal boundaries at unequal
temperatures, well known as the Horton–Rogers–Lapwood problem, is revisited including the effect of pressure work and viscous
dissipation in the local energy balance. A linear stability analysis of rolls disturbances is performed. The analysis shows
that, while the contribution of viscous dissipation is ineffective, the contribution of the pressure work may be important.
The condition of marginal stability is investigated by adopting two solution procedures: method of weighted residuals and
explicit Runge–Kutta method. The pressure work term in the energy balance yields an increase of the value of the Darcy–Rayleigh
number at marginal stability. In other words, the effect of pressure work is a stabilizing one. Furthermore, while the critical
value of the Darcy– Rayleigh number may be considerably affected by the pressure work contribution, the critical value of
the wave number is affected only in rather extreme cases, i.e. for very high values of the Gebhart number. A nonlinear stability
analysis is also performed pointing out that the joint effects of viscous dissipation and pressure work result in a reduction
of the excess Nusselt number due to convection, when the Darcy–Rayleigh number is replaced by the superadiabatic Darcy–Rayleigh
number. 相似文献
39.
研究了在R 3 ![]()
![]()
中有界区域内相互作用的Forchheimer-Darcy流体方程组解的结构稳定性。假设黏性流体在Ω 1 ![]()
![]()
中满足Forchheimer方程组,在Ω 2 ![]()
![]()
中满足Darcy方程组,借助于一些先验估计,构造了微分不等式,证明了对Forchheimer系数b ![]()
![]()
,Forchheimer-Darcy方程组的解是收敛的。 相似文献
40.
This work presents an approach towards resolving hydrodynamic flow in real porous media by carrying out direct numerical simulations in the reconstructed macroporous (flow-through) domain of a silica monolith. The macroporous domain of a 60 μm × 60 μm × 12 μm segment of a 100 μm i.d. capillary silica monolith was reconstructed by confocal laser scanning microscopy. A 60 μm × 12 μm × 12 μm segment of the reconstructed domain was then used as the 3D matrix for simulation of fluid flow by the lattice-Boltzmann method on a high-performance computing platform. Excellent agreement is observed between the experimental and simulated Darcy permeabilities without any assumptions or further adjustments on the monolith morphology. The flow velocity field is analyzed in detail, including longitudinal and transverse velocity distributions, the occurrence of negative longitudinal velocities, as well as the beginning transition to the viscous-inertial flow regime. The presented methodology promises great potential for resolving the key relationships between morphology and band broadening in monolithic columns for HPLC applications. 相似文献