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.

A NEW IMMERSED BOUNDARY-LATTICE BOLTZMANN METHOD AND ITS APPLICATION TO INCOMPRESSIBLE FLOWS

2009 ◽  
Vol 23 (03) ◽  
pp. 261-264 ◽  
Author(s):  
CHANG SHU ◽  
JIE WU
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Incompressible Flows ◽  
Slip Boundary Condition ◽  
Circular Cylinders ◽  
Immersed Boundary ◽  
Restoring Force ◽  
Slip Boundary ◽  
Boltzmann Method

A new immersed boundary-lattice Boltzmann method (IB-LBM) is presented in this work. In the conventional IB-LBM, the restoring force is pre-calculated, which makes the non-slip boundary condition to be only approximately satisfied. As a result, the streamline penetration to the solid body occurs. In the present study, the velocity correction (restoring force) is considered as unknown. It is determined in such a way that the non-slip boundary condition is enforced. As compared with conventional IB-LBM, the solution procedure of current IB-LBM is almost the same except that the non-slip boundary condition is guaranteed in the present scheme while it is only approximately satisfied in the conventional scheme. Numerical results for simulation of flows over fixed circular cylinders showed that the present method can provide accurate solutions without any streamline penetration phenomenon.

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.

ELECTROKINETIC SLIP FLOW OF MICROFLUIDICS IN TERMS OF STREAMING POTENTIAL BY A LATTICE BOLTZMANN METHOD: A BOTTOM-UP APPROACH

2007 ◽  
Vol 18 (04) ◽  
pp. 693-700 ◽  
Author(s):  
XIN FU ◽  
BAOMING LI ◽  
JUNFENG ZHANG ◽  
FUZHI TIAN ◽  
DANIEL Y. KWOK
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Slip Boundary ◽  
Surface Energetics ◽  
Boltzmann Method

In traditional computational fluid dynamics, the effect of surface energetics on fluid flow is often ignored or translated into an arbitrary selected slip boundary condition in solving the Navier-Stokes equation. Using a bottom-up approach, we show in this paper that variation of surface energetics through intermolecular theory can be employed in a lattice Boltzmann method to investigate both slip and non-slip phenomena in microfluidics in conjunction with the description of electrokinetic phenomena for electrokinetic slip flow. Rather than using the conventional Navier-Stokes equation with a slip boundary condition, the description of electrokinetic slip flow in microfluidics is manifested by the more physical solid-liquid energy parameters, electrical double layer and contact angle in the mean-field description of the lattice Boltzmann method.

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.

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