scholarly journals CREEPING FLOW PAST A POROUS APPROXIMATELY SPHERICAL SHELL: STRESS JUMP BOUNDARY CONDITION

2011 ◽  
Vol 52 (3) ◽  
pp. 289-300 ◽  
Author(s):  
D. SRINIVASACHARYA ◽  
M. KRISHNA PRASAD
Keyword(s):  
Boundary Condition ◽  
Spherical Shell ◽  
Stokes Equations ◽  
Jump Condition ◽  
Creeping Flow ◽  
Navier Stokes ◽  
Free Fluid ◽  
Stress Jump ◽  
Navier Stokes Equations ◽  
Stress Jump Boundary Condition

AbstractThe creeping flow of an incompressible viscous liquid past a porous approximately spherical shell is considered. The flow in the free fluid region outside the shell and in the cavity region of the shell is governed by the Navier–Stokes equations. The flow within the porous annular region of the shell is governed by Brinkman’s model. The boundary conditions used at the interface are continuity of the velocity, continuity of the pressure and Ochoa-Tapia and Whitaker’s stress jump condition. An exact solution for the problem and an expression for the drag on the porous approximately spherical shell are obtained. The drag is evaluated numerically for several values of the parameters governing the flow.

Creeping Flow Relative to a Porous Spherical Shell

2000 ◽  
Vol 16 (3) ◽  
pp. 137-143
Author(s):  
Ming-Da Chen ◽  
Wang-Long Li
Keyword(s):  
Spherical Shell ◽  
Stokes Equations ◽  
Creeping Flow ◽  
Free Fluid ◽  
Fluid Interfaces ◽  
Stress Jump ◽  
The Core ◽  
Porous Spherical Shell ◽  
Darcy Equations ◽  
Shell Region

ABSTRACTIn this study, the problem of creeping flow relative to an isolated porous spherical shell has been examined. The Brinkman-extended Darcy equations and the Stokes' equations are utilized to model the flow in the porous region (shell region) and free fluid region (inside the core and outside the shell), respectively. The stress jump boundary conditions at the porous media/free fluid interfaces are included and the exact solution has been found. The drag experienced by the porous shell has been discussed for various jump parameters and shell thickness.

scholarly journals Involving the Navier–Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2184-2192 ◽  
Author(s):  
Joris C. G. Verschaeve
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Grid Spacing ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Boltzmann Method

By means of the continuity equation of the incompressible Navier–Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

Natural Convection in a Cavity Partially Filled with a Vertical Porous Medium

2011 ◽  
Vol 321 ◽  
pp. 15-18 ◽  
Author(s):  
Fang Liu ◽  
Bao Ming Chen
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Boundary Condition ◽  
Porous Medium ◽  
Nusselt Number ◽  
Free Fluid ◽  
Stress Jump ◽  
Convection And Heat Transfer ◽  
Flow And Heat Transfer ◽  
Stress Jump Boundary Condition

The shear stress jump boundary condition that must be imposed at an interface between a porous medium and a free fluid in an enclosure is investigated. Two-domain approach is founded and finite element method is used to solve the problem. Three stress jump coefficients 0, 1, -1 are analyzed for different Rayleigh number, permeability and thickness of porous layer. Variation of Maximum stream function and Nusselt number show stronger convection and heat transfer when the stress jump coefficient is positive. There is little distinctive in flow and heat transfer when the value of coefficient is equal to 0 and -1.

NUMERICAL SIMULATION OF FREE VORTEX WITH MODIFIED NAVIER–STOKES CHARACTERISTIC BOUNDARY CONDITIONS

2010 ◽  
Vol 24 (13) ◽  
pp. 1333-1336
Author(s):  
LIN CHEN ◽  
DENGBIN TANG ◽  
XIN GUO
Keyword(s):  
Boundary Condition ◽  
Compressible Flows ◽  
Diffusion Processes ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Free Vortex ◽  
Navier Stokes Equations ◽  
Characteristic Boundary ◽  
Accurate Treatment ◽  
Characteristic Boundary Condition

The convection and diffusion processes of free vortex in compressible flows are simulated by using high precision numerical method to solve for the Navier–Stokes equations. Accurate treatment of the boundary condition is extremely important for simulation of vortex flows. The developed numerical methods are well presented by combining six-order non-dissipation compact schemes with Navier–Stokes characteristic boundary condition having transverse and viscous terms, and can accurately simulate the movement of free vortex. The numerical reflecting waves at the boundaries are well controlled.

A New Partial Slip Boundary Condition for the Lattice-Boltzmann Method

2013 ◽  
Author(s):  
Marc-Florian Uth ◽  
Alf Crüger ◽  
Heinz Herwig
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Slip Model ◽  
Navier Stokes Equations ◽  
Navier Slip ◽  
Slip Boundary ◽  
Boltzmann Method

In micro or nano flows a slip boundary condition is often needed to account for the special flow situation that occurs at this level of refinement. A common model used in the Finite Volume Method (FVM) is the Navier-Slip model which is based on the velocity gradient at the wall. It can be implemented very easily for a Navier-Stokes (NS) Solver. Instead of directly solving the Navier-Stokes equations, the Lattice-Boltzmann method (LBM) models the fluid on a particle basis. It models the streaming and interaction of particles statistically. The pressure and the velocity can be calculated at every time step from the current particle distribution functions. The resulting fields are solutions of the Navier-Stokes equations. Boundary conditions in LBM always not only have to define values for the macroscopic variables but also for the particle distribution function. Therefore a slip model cannot be implemented in the same way as in a FVM-NS solver. An additional problem is the structure of the grid. Curved boundaries or boundaries that are non-parallel to the grid have to be approximated by a stair-like step profile. While this is no problem for no-slip boundaries, any other velocity boundary condition such as a slip condition is difficult to implement. In this paper we will present two different implementations of slip boundary conditions for the Lattice-Boltzmann approach. One will be an implementation that takes advantage of the microscopic nature of the method as it works on a particle basis. The other one is based on the Navier-Slip model. We will compare their applicability for different amounts of slip and different shapes of walls relative to the numerical grid. We will also show what limits the slip rate and give an outlook of how this can be avoided.

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