The immersed boundary projection method for the Navier slip boundary condition

2019 ◽  
Vol 2019 (0) ◽  
pp. OS2-25
Author(s):  
Takehiro FUJII ◽  
Takeshi OMORI ◽  
Takeo KAJISHIMA
Keyword(s):  
Boundary Condition ◽  
Projection Method ◽  
Slip Boundary Condition ◽  
Immersed Boundary ◽  
Navier Slip ◽  
Slip Boundary ◽  
Boundary Projection

Numerical Simulation of Newtonian Fluid Flow in a T-Channel with no Slip/Slip Boundary Conditions on a Solid Wall

2017 ◽  
Vol 743 ◽  
pp. 480-485
Author(s):  
Evgeny Borzenko ◽  
Olga Dyakova
Keyword(s):  
Boundary Condition ◽  
Fluid Flow ◽  
Solid Wall ◽  
Simple Procedure ◽  
Slip Boundary Condition ◽  
Navier Slip ◽  
Slip Boundary ◽  
Pressure Profiles ◽  
Slip Yield Stress ◽  
Solid Walls

The planar flow of a Newtonian incompressible fluid in a T-shaped channel is investigated. Three fluid interaction models with solid walls are considered: no slip boundary condition, Navier slip boundary condition and slip boundary condition with slip yield stress. The fluid flow is provided by uniform pressure profiles at the boundary sections of the channel. The problem is numerically solved using a finite difference method based on the SIMPLE procedure. Characteristic flow regimes have been found for the described models of liquid interaction with solid walls. The estimation of the influence of the Reynolds number, pressure applied to the boundary sections and the parameters of these models on the flow pattern was performed. The criterial dependences describing main characteristics of the flow under conditions of the present work have been demonstrated.

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.

scholarly journals Sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact lines

2018 ◽  
Vol 849 ◽  
pp. 805-833 ◽  
Author(s):  
Xianmin Xu ◽  
Yana Di ◽  
Haijun Yu
Keyword(s):  
Boundary Condition ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Slip Boundary Condition ◽  
Sharp Interface ◽  
Navier Slip ◽  
Slip Boundary ◽  
Moving Contact ◽  
Moving Contact Lines

The sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for binary fluids with moving contact lines are studied by asymptotic analysis and numerical simulations. The effects of the mobility number as well as a phenomenological relaxation parameter on the boundary condition are considered. In asymptotic analysis, we consider both the cases that the mobility number is proportional to the Cahn number and the square of the Cahn number, and derive the sharp-interface limits for several set-ups of the boundary relaxation parameter. It is shown that the sharp-interface limit of the phase-field model is the standard two-phase incompressible Navier–Stokes equations coupled with several different slip boundary conditions. Numerical results are consistent with the analysis results and also illustrate the different convergence rates of the sharp-interface limits for different scalings of the two parameters.

Particle Sedimentation in a Constricted Passage Using a Flexible Forcing IB-LBM Scheme

2015 ◽  
Vol 12 (01) ◽  
pp. 1350095 ◽  
Author(s):  
S. M. Dash ◽  
T. S. Lee ◽  
H. Huang
Keyword(s):  
Boundary Condition ◽  
Moving Boundary ◽  
Correction Term ◽  
Slip Boundary Condition ◽  
Lattice Boltzmann Model ◽  
Computational Time ◽  
Immersed Boundary ◽  
Force Density ◽  
Time Step ◽  
Slip Boundary

A novel flexible forcing hybrid immersed boundary-lattice Boltzmann model (IB-LBM) is introduced in the present paper for solving moving boundary problems. In conventional IB-LBM schemes, explicit formulations of force density term may not ensure no-slip boundary condition accurately, which leads to inaccurate force and torque calculations for moving object. Following an implicit force density calculation, a single Lagrangian velocity correction term is advised in this study. The formula for this correction term is much simpler and with the help of flexible number of sub-iteration/forcing, the computational time is significantly saved. The no-slip boundary condition is achieved accurately within a convergence limit. The proposed algorithm shows advantages for unsteady and moving boundary problem, where boundary convergence is satisfied consistently at every time step. In particular, a 2D particulate flow case is simulated in a constricted channel. Interesting observations and results are discussed in this article.

A Boundary Condition-Implemented Immersed Boundary-Lattice Boltzmann Method and Its Application for Simulation of Flows Around a Circular Cylinder

2014 ◽  
Vol 6 (06) ◽  
pp. 811-829 ◽  
Author(s):  
X. Wang ◽  
C. Shu ◽  
J. Wu ◽  
L. M. Yang
Keyword(s):  
Boundary Condition ◽  
Circular Cylinder ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Delta Function ◽  
Slip Boundary Condition ◽  
Immersed Boundary ◽  
First Order ◽  
Slip Boundary ◽  
Boltzmann Method

AbstractA boundary condition-implemented immersed boundary-lattice Boltzmann method (IB-LBM) is presented in this work. The present approach is an improvement to the conventional IB-LBM. In the conventional IB-LBM, the no-slip boundary condition is only approximately satisfied. As a result, there is flow penetration to the solid boundary. Another drawback of conventional IB-LBM is the use of Dirac delta function interpolation, which only has the first order of accuracy. In this work, the no-slip boundary condition is directly implemented, and used to correct the velocity at two adjacent mesh points from both sides of the boundary point. The velocity correction is made through the second-order polynomial interpolation rather than the first-order delta function interpolation. Obviously, the two drawbacks of conventional IB-LBM are removed in the present study. Another important contribution of this paper is to present a simple way to compute the hydrodynamic forces on the boundary from Newton’s second law. To validate the proposed method, the two-dimensional vortex decaying problem and incompressible flow over a circular cylinder are simulated. As shown in the present results, the flow penetration problem is eliminated, and the obtained results compare very well with available data in the literature.

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