Flow of a viscous incompressible fluid after a sudden point impulse near a wall

2009 ◽  
Vol 629 ◽  
pp. 425-443 ◽  
Author(s):  
B. U. FELDERHOF
Keyword(s):  
Boundary Condition ◽  
Incompressible Fluid ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Short Time ◽  
Short Times

The flow of a viscous incompressible fluid generated by a sudden impulse near a wall with no-slip boundary condition is studied on the basis of the linearized Navier–Stokes equations. It turns out that the flow differs significantly from that for the perfect slip boundary condition, except far from the wall and at short times. At short time the flow is irrotational and can be described by a potential which varies with the square root of time. Correspondingly the pressure disturbance is quite large at short times. It shows an oscillation at later times if the impulse is directed parallel to the wall and decays monotonically for impulse perpendicular to the wall.

Transient flow of a viscous incompressible fluid in a circular tube after a sudden point impulse

2009 ◽  
Vol 637 ◽  
pp. 285-303 ◽  
Author(s):  
B. U. FELDERHOF
Keyword(s):  
Incompressible Fluid ◽  
Transient Flow ◽  
Stokes Equations ◽  
Circular Tube ◽  
Viscous Incompressible Fluid ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Long Time

The flow of a viscous incompressible fluid in a circular tube generated by a sudden impulse on the axis is studied on the basis of the linearized Navier–Stokes equations. A no-slip boundary condition is assumed to hold on the wall of the tube. At short time the flow is irrotational and may be described by a potential which varies with the square root of time. At later times there is a sequence of moving and decaying vortex rings. At long times the flow velocity decays with an algebraic long-time tail. The impulse generates a time-dependent pressure difference between the ends of the tube.

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.

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.

Transient flow of a viscous compressible fluid in a circular tube after a sudden point impulse

2010 ◽  
Vol 644 ◽  
pp. 97-106 ◽  
Author(s):  
B. U. FELDERHOF
Keyword(s):  
Compressible Fluid ◽  
Transient Flow ◽  
Stokes Equations ◽  
Circular Tube ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Viscous Compressible Fluid ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Short Time

The flow of a viscous compressible fluid in a circular tube generated by a sudden impulse at a point on the axis is studied on the basis of the linearized Navier–Stokes equations. A no-slip boundary condition is assumed to hold on the wall of the tube. Owing to the finite velocity of sound the flow behaviour differs qualitatively from that of an incompressible fluid. The flow velocity and the pressure disturbance at any fixed point different from the source point vanish at short time and decay at long times with a t−3/2 power law.

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