Pressure condition for lattice Boltzmann methods on domains with curved boundaries

AbstractWe propose a lattice Boltzmann algorithm for an average pressure boundary condition at outlets in pipe flow systems. The advantage of this boundary condition is that only the average pressure is used to recover the non-trivial flow fields. The asymptotic analysis shows that this algorithm works for general curved boundaries and renders a second order accurate velocity and a first order accurate pressure approximation of the incompressible Navier–Stokes solution. Here, we verify the accuracy by numerical simulations of a Poiseuille flow and a less symmetric flow with non-trivial pressure field in channels inclined with arbitrary angle, and flows in a pipe with three outlets

DSMC-LBM mapping scheme for rarefied and non-rarefied gas flows

We present the formulation of a kinetic mapping scheme between the Direct Simulation Monte Carlo (DSMC) and the Lattice Boltzmann Method (LBM) which is at the basis of the hybrid model used to couple the two methods in view of efficiently and accurately simulate isothermal flows characterized by variable rarefaction effects. Owing to the kinetic nature of the LBM, the procedure we propose ensures to accurately couple DSMC and LBM at a larger Kn number than usually done in traditional hybrid DSMC-Navier-Stokes equation models. We show the main steps of the mapping algorithm and illustrate details of the implementation. Good agreement is found between the moments of the single particle distribution function as obtained from the mapping scheme and from independent LBM or DSMC simulations at the grid nodes where the coupling is imposed. We also show results on the application of the hybrid scheme based on a simpler mapping scheme for plane Poiseuille flow at finite Kn number. Potential gains in the computational efficiency assured by the application of the coupling scheme are estimated for the same flow.Comment: Submitted to Journal of Computational Scienc

Moment-based formulation of Navier–Maxwell slip boundary conditions for lattice Boltzmann simulations of rarefied flows in microchannels

We present an implementation of first-order Navier–Maxwell slip boundary conditions for simulating near-continuum rarefied flows in microchannels with the lattice Boltzmann method. Rather than imposing boundary conditions directly on the particle velocity distribution functions, following the existing discrete analogs of the specular and diffuse reflection conditions from continuous kinetic theory, we use a moment-based method to impose the Navier–Maxwell slip boundary conditions that relate the velocity and the strain rate at the boundary. We use these conditions to solve for the unknown distribution functions that propagate into the\ud domain across the boundary. We achieve second-order accuracy by reformulating these conditions for the second set of distribution functions that arise in the derivation of the lattice Boltzmann method by an integration along characteristics. The results are in excellent agreement with asymptotic solutions of the compressible Navier-Stokes equations for microchannel flows in the slip regime. Our moment formalism is also valuable for analysing the existing boundary conditions, and explains the origin of numerical slip in the bounce-back and other common boundary conditions that impose explicit conditions on the higher moments instead of on the local tangential velocity

A comparative study of boundary conditions for lattice Boltzmann simulations of high Reynolds number flows

Four commonly-used boundary conditions in lattice Boltzmann simulation, i.e. the bounce-back, non-equilibrium bounce-back, non-equilibrium extrapolation, and the kinetic boundary condition, have been systematically investigated to assess their accuracy, stability and efficiency in simulating high Reynolds number flows. For the classical lid-driven cavity flow problem, it is found that the bounce-back scheme does not influence the simulation accuracy in the bulk region if the boundary condition is properly implemented to avoid generating non-physical slip velocity. Although the kinetic boundary condition naturally produces physical slip velocity at the wall, it gives overall satisfactory predictions of the center-line velocity profile and the vortex center locations for the Reynolds numbers considered. For the cavity flow problem, all four boundary conditions show minimal difference in the computing time needed to reach a steady state. This is surprising because the kinetic boundary condition is significantly different from the other three schemes which are designed specifically for no-slip boundary conditions. The bounce-back scheme is the most computationally efficient in updating boundary points, which is particularly attractive if there are a large number of solid bodies in the flow field. For the numerical stability, we further test the pressure-driven channel flow with or without a enclosed square cylinder. Overall, the kinetic boundary condition is the most stable of the four schemes. The non-equilibrium extrapolation scheme presents excellent stability second to the kinetic boundary condition for the lid-driven cavity flow. In comparison with other threes schemes, the stability of non-equilibrium bounce-back scheme appears to be less satisfactory for both flows

Accurate permeability prediction in tight gas rocks via lattice Boltzmann simulations with an improved boundary condition

Accurately predicting gas transport in rocks is required for enhancing the accuracy of field production models. The mesoscale lattice Boltzmann (LB) method can be implemented to predict gas permeability in porous rocks. However, the published LB results for the Klinkenberg effect are often inconsistent with the widely used Beskok-Karniadakis-Civan's (BKC's) correlation. The culprit of the unphysical effect has been identified in the typically implemented boundary conditions (BCs). An improved BC is proposed herein to reliably predict gas permeability. Non-equilibrium molecular dynamics simulations are conducted to benchmark the proposed approach. The results show that the presented LB predictions for the Klinkenberg effect are quantitatively consistent with experimental data and the BKC's correlation, indicating that the unphysical effects have been minimized. More importantly, a numerical consistency is achieved for describing the Klinkenberg effect at molecular through macroscopic scales. These observations are relevant for improving our ability to predict gas production from tight formations

Lattice Boltzmann simulations of pressure-driven flows in microchannels using Navier-Maxwell slip boundary conditions

We present lattice Boltzmann simulations of rarefied flows driven by pressure drops along two-dimensional microchannels. Rarefied effects lead to non-zero cross-channel velocities, and nonlinear variations in the pressure along the channel. Both effects are absent in flows driven by uniform body forces. We obtain second-order accuracy for the two components of velocity and the pressure relative to asymptotic solutions of the compressible Navier–Stokes equations with slip boundary conditions. Since the common lattice Boltzmann formulations cannot capture Knudsen boundary layers, we replace the usual discrete analogs of the specular and diffuse reflection conditions from continuous kinetic theory with a moment-based implementation of the first-order Navier–Maxwell slip boundary conditions that relate the tangential velocity to the strain rate at the boundary. We use these conditions to solve for the unknown distribution functions that propagate into the domain across the boundary. We achieve second-order accuracy by reformulating these conditions for the second set of distribution functions that arise in the derivation of the lattice Boltzmann method by an integration along characteristics. Our moment formalism is also valuable for analysing the existing boundary conditions. It reveals the origin of numerical slip in the bounce-back and other common boundary conditions that impose conditions on the higher moments, not on the local tangential velocity itself

Arbitrary slip length for fluid-solid interface of arbitrary geometry in smoothed particle dynamics

We model a slip boundary condition at fluid-solid interface of an arbitrary geometry in smoothed particle hydrodynamics and smoothed dissipative particle dynamics simulations. Under an assumption of linear profile of the tangential velocity at quasi-steady state near the interface, an arbitrary slip length $b$ can be specified and correspondingly, an artificial velocity for every boundary particle can be calculated. Therefore, $b$ as an input parameter affects the calculation of dissipative and random forces near the interface. For $b \to 0$, the no-slip is recovered while for $b \to \infty$, the free-slip is achieved. Technically, we devise two different approaches to calculate the artificial velocity of any boundary particle. The first has a succinct principle and is competent for simple geometries, while the second is subtle and affordable for complex geometries. Slip lengths in simulations for both steady and transient flows coincide with the expected ones. As demonstration, we apply the two approaches extensively to simulate curvy channel flows, dynamics of an ellipsoid in pipe flow and flows within complex microvessels, where desired slip lengths at fluid-solid interfaces are prescribed. The proposed methodology may apply equally well to other particle methods such as dissipative particle dynamics and moving particle semi-implicit methods