scholarly journals Numerical Simulations of Flows in a Cerebral Aneurysm Using the Lattice Boltzmann Method with the Half-Way and Interpolated Bounce-Back Schemes

Fluids ◽  
2021 ◽  
Vol 6 (10) ◽  
pp. 338
Author(s):  
Susumu Osaki ◽  
Kosuke Hayashi ◽  
Hidehito Kimura ◽  
Takeshi Seta ◽  
Takashi Sasayama ◽  
...  
Keyword(s):  
Experimental Data ◽  
Cerebral Aneurysm ◽  
Lattice Boltzmann ◽  
Flow Simulation ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
Lattice Boltzmann Simulations ◽  
Complex Boundary ◽  
Boltzmann Method ◽  
Bounce Back

Lattice Boltzmann simulations and a velocity measurement of flows in a cerebral aneurysm reconstructed from MRA (magnetic resonance angiography) images of an actual aneurysm were carried out and the numerical results obtained using the bounce-back schemes were compared with the experimental data to discuss the effects of the numerical treatment of the no-slip boundary condition of the complex boundary shape of the aneurysm on the predictions. The conclusions obtained are as follows: (1) measured data of the velocity in the aneurysm model useful for validation of numerical methods were obtained, (2) the numerical stability of the quadratic interpolated bounce-back scheme (QBB) in the flow simulation of the cerebral aneurysm is lower than those of the half-way bounce-back (HBB) and the linearly interpolated bounce-back (LBB) schemes, (3) the flow structures predicted using HBB and LBB are comparable and agree well with the experimental data, and (4) the fluctuations of the wall shear stress (WSS), i.e., the oscillatory shear index (OSI), can be well predicted even with the jaggy wall representation of HBB, whereas the magnitude of WSS predicted with HBB tends to be smaller than that with LBB.

Examination of the Slip Boundary Condition by µ-PIV and Lattice Boltzmann Simulations

2002 ◽  
Author(s):  
Derek C. Tretheway ◽  
Luoding Zhu ◽  
Linda Petzold ◽  
Carl D. Meinhart
Keyword(s):  
Boundary Condition ◽  
Shear Rate ◽  
Channel Flow ◽  
Lattice Boltzmann ◽  
Slip Velocity ◽  
Slip Length ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
Lattice Boltzmann Simulations ◽  
Bounce Back

This work examines the slip boundary condition by Lattice Boltzmann simulations, addresses the validity of the Navier’s hypothesis that the slip velocity is proportional to the shear rate and compares the Lattice Boltzmann simulations to the experimental results of Tretheway and Meinhart (Phys. of Fluids, 14, L9–L12). The numerical simulation models the boundary condition as the probability, P, of a particle to bounce-back relative to the probability of specular reflection, 1−P. For channel flow, the numerically calculated velocity profiles are consistent with the experimental profiles for both the no-slip and slip cases. No-slip is obtained for a probability of 100% bounce-back, while a probability of 0.03 is required to generate a slip length and slip velocity consistent with the experimental results of Tretheway and Meinhart for a hydrophobic surface. The simulations indicate that for microchannel flow the slip length is nearly constant along the channel walls, while the slip velocity varies with wall position as a results of variations in shear rate. Thus, the resulting velocity profile in a channel flow is more complex than a simple combination of the no-slip solution and slip velocity as is the case for flow between two infinite parallel plates.

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.

scholarly journals Immersed boundary (IB) - Lattice Boltzmann Method (LBM) coupled with Adaptive MESH Refinement (AMR) techniques for simulation of Incompressible Viscous Flow

2021 ◽  
Author(s):  
Xixiong Guo
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Adaptive Mesh Refinement ◽  
Moving Objects ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Slip Boundary Condition ◽  
Immersed Boundary ◽  
Slip Boundary ◽  
Boltzmann Method

This study is aimed at developing a novel computational framework that seamlessly incorporates the feedback forcing model and adaptive mesh refinement mesh refinement (AMR) techniques in the immersed-boundary (IB) lattice Boltzmann method (LBM) approach, so that challenging problems, including the interactions between flowing fluids and moving objects, can be numerically investigated. Owing to the feedback forcing based IB model, the advantages, such as simple mechanics principle, explicit interpolations, and inherent satisfaction of no-slip boundary condition for solid surfaces are fully exhibited. Additionally, the "bubble' function is employed in the local mesh refinement process, so that the solution of second order accuracy at newly generated nodes can be obtained only by the spatial interpolation but no temporal interpolation. Focusing on both steady and unsteady flow around a single cylinder and bi-cylinders, a number of test cases performed in this study have demonstrated the usefulness and effectiveness of the present AMR IB-LBM approach.

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.

AN ELASTIC-COLLISION SCHEME FOR LATTICE BOLTZMANN METHODS

2001 ◽  
Vol 12 (03) ◽  
pp. 387-401 ◽  
Author(s):  
J. G. ZHOU
Keyword(s):  
Experimental Data ◽  
Lattice Boltzmann ◽  
Elastic Collision ◽  
Complex Geometries ◽  
Slip Boundary Conditions ◽  
Lattice Boltzmann Methods ◽  
Slip Boundary ◽  
Arbitrary Complex ◽  
Bounce Back ◽  
Good Agreement

An elastic-collision scheme is developed to achieve slip and semi-slip boundary conditions for lattice Boltzmann methods. Like the bounce-back scheme, the proposed scheme is efficient, robust and generally suitable for flows in arbitrary complex geometries. It involves an equivalent level of computation effort to the bounce-back scheme. The new scheme is verified by predicting wind-driven circulating flows in a dish-shaped basin and a flow in a strongly bent channel, showing good agreement with analytical solutions and experimental data. The capability of the scheme for simulating flows through multiple bodies has also been demonstrated.

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