Multiscale MD/LBM Simulations of Flow in Complex Nano/Micro Channels

2010 ◽  
Author(s):  
D. D. Marsh ◽  
S. P. Vanka
Keyword(s):  
Molecular Dynamics ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Velocity Slip ◽  
Navier Stokes ◽  
Graphics Processor ◽  
Micro Channels ◽  
Hybrid Code ◽  
Hybrid Solver ◽  
Complex Boundaries

This paper examines the fluid behavior in micro and nano sized channels by using a coupled Molecular Dynamics and Lattice Boltzmann solution method, implemented in a novel fashion on a Graphics Processor. Molecular Dynamics is well known for its ability to resolve phenomena in the near wall regions, where continuum assumptions are no longer valid, at the expense of computational power. Lattice Boltzmann is a mesoscale continuum-description solver that is very efficient and reduces to the Navier-Stokes equations, thereby being a logical choice to solve regions further from the wall. This method is parallelized to be run on the Graphics Processor, using NVIDIA’s CUDA programming language. Individually, Lattice Boltzmann methods are approximately 70× faster on the GPU than a modern CPU, Molecular Dynamics is about 5× faster. Higher resolutions are able to be simulated than previously performed due to the efficiency of this implementation. We analyze the results of straight channel Poiseuille flow using the hybrid solver and note the continuum breakdown is successfully predicted by the hybrid code in the form of density oscillations near the wall along with velocity slip conditions. Streamlines, contours and velocity profiles are utilized to illustrate these points. Future work includes expanding this solver’s capability to handle complex boundaries.

scholarly journals Dynamic Domain Decomposition Strategy Coupling Lattice Boltzmann Methods With Finite Differences Approximations of the Navier-Stokes Equations to Study Bodies in Current

2015 ◽  
Author(s):  
Giuseppina Colicchio ◽  
Claudio Lugni ◽  
Marilena Greco ◽  
Odd M. Faltinsen
Keyword(s):  
Domain Decomposition ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Dynamic Change ◽  
Accurate Solution ◽  
The Body ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Coupling Strategy ◽  
Hybrid Solver

A Domain-Decomposition (DD) strategy is proposed for problems involving regions with slow variations of the flow (A) and others where the fluid features undergo rapid changes (B), like in the case of steady current past bodies with pronounced local unsteadiness connected with the vortex shedding from the structures. For an efficient and accurate solution of such problems, the DD couples a Finite Difference solver of the Navier-Stokes equations (FD-NS) with a Multiple Relaxation Time Lattice Boltzmann method (MRT-LBM). Regions A are handled by FD-NS, while zones B are solved by MRT-LBM and the two solvers exchange information within a strong coupling strategy. Present DD strategy is able to deal with a dynamic change of the sub-domains topology. This feature is needed when regions with vorticity shed from the body vary in time for a more flexible and reliable solution strategy. Its performances in terms of accuracy and efficiency have been successfully assessed by comparing the hybrid solver against a full FD-NS solution and experimental data for a 2D circular cylinder in an impulsively started flow.

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.

Relationship between accuracy and number of velocity particles of the finite-difference lattice Boltzmann method in velocity slip simulations

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
Minoru Watari
Keyword(s):  
Relaxation Process ◽  
Stokes Equations ◽  
Velocity Slip ◽  
Simulation Models ◽  
Knudsen Layer ◽  
Navier Stokes ◽  
Flow Area ◽  
Navier Stokes Equations ◽  
Conservation Of Momentum ◽  
Boltzmann Method

Relationship between accuracy and number of velocity particles in velocity slip phenomena was investigated by numerical simulations and theoretical considerations. Two types of 2D models were used: the octagon family and the D2Q9 model. Models have to possess the following four prerequisites to accurately simulate the velocity slip phenomena: (a) equivalency to the Navier–Stokes equations in the N-S flow area, (b) conservation of momentum flow Pxy in the whole area, (c) appropriate relaxation process in the Knudsen layer, and (d) capability to properly express the mass and momentum flows on the wall. Both the octagon family and the D2Q9 model satisfy conditions (a) and (b). However, models with fewer velocity particles do not sufficiently satisfy conditions (c) and (d). The D2Q9 model fails to represent a relaxation process in the Knudsen layer and shows a considerable fluctuation in the velocity slip due to the model’s angle to the wall. To perform an accurate velocity slip simulation, models with sufficient velocity particles, such as the triple octagon model with moving particles of 24 directions, are desirable.

scholarly journals Event-Driven Molecular Dynamics Simulation of Hard-Sphere Gas Flows in Microchannels

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Volkan Ramazan Akkaya ◽  
Ilyas Kandemir
Keyword(s):  
Molecular Dynamics ◽  
Hard Sphere ◽  
Stokes Equations ◽  
Hard Spheres ◽  
Flow Characteristics ◽  
Dynamics Simulation ◽  
Navier Stokes ◽  
Gas Flows ◽  
Linearized Boltzmann Equation ◽  
Event Driven

Classical solution of Navier-Stokes equations with nonslip boundary condition leads to inaccurate predictions of flow characteristics of rarefied gases confined in micro/nanochannels. Therefore, molecular interaction based simulations are often used to properly express velocity and temperature slips at high Knudsen numbers (Kn) seen at dilute gases or narrow channels. In this study, an event-driven molecular dynamics (EDMD) simulation is proposed to estimate properties of hard-sphere gas flows. Considering molecules as hard-spheres, trajectories of the molecules, collision partners, corresponding interaction times, and postcollision velocities are computed deterministically using discrete interaction potentials. On the other hand, boundary interactions are handled stochastically. Added to that, in order to create a pressure gradient along the channel, an implicit treatment for flow boundaries is adapted for EDMD simulations. Shear-Driven (Couette) and Pressure-Driven flows for various channel configurations are simulated to demonstrate the validity of suggested treatment. Results agree well with DSMC method and solution of linearized Boltzmann equation. At low Kn, EDMD produces similar velocity profiles with Navier-Stokes (N-S) equations and slip boundary conditions, but as Kn increases, N-S slip models overestimate slip velocities.

A PLATFORM FOR DEVELOPING NEW LATTICE BOLTZMANN MODELS

2005 ◽  
Vol 16 (01) ◽  
pp. 61-84 ◽  
Author(s):  
H. W. ZHENG ◽  
C. SHU ◽  
Y. T. CHEW ◽  
J. QIU
Keyword(s):  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Cavity Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Velocity Models ◽  
Equilibrium Function ◽  
New Models ◽  
Lattice Boltzmann Models

This paper presents a platform to develop new lattice Boltzmann models. It gives a general framework for different applications. It also presents basic velocity models and a set of basic conditions to construct new models which can recover Navier–Stokes equations. Besides, the equilibrium function can be easily obtained through a set of equations. By using the platform, we can easily recover the existing models. Some new models are derived from the platform and validated by their application to simulate the two-dimensional driven cavity flow. The obtained numerical results agree very well with available data in the literature.

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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