Computation of transient viscous flows using indirect radial basis function networks

In this paper, an indirect/integrated radial-basis-function network (IRBFN) method is further developed to solve transient partial differential equations (PDEs) governing fluid flow problems. Spatial derivatives are discretized using one- and two-dimensional IRBFN interpolation schemes, whereas temporal derivatives are approximated using a method of lines and a finite-difference technique. In the case of moving interface problems, the IRBFN method is combined with the level set method to capture the evolution of the interface. The accuracy of the method is investigated by considering several benchmark test problems, including the classical lid-driven cavity flow. Very accurate results are achieved using relatively low numbers of data points

Analysis of the incompressibility constraint in the Smoothed Particle Hydrodynamics method

Smoothed particle hydrodynamics is a particle-based, fully Lagrangian, method for fluid-flow simulations. In this work, fundamental concepts of the method are first briefly recalled. Then, we present a thorough comparison of three different incompressibility treatments in SPH: the weakly compressible approach, where a suitably-chosen equation of state is used; and two truly incompressible methods, where the velocity field projection onto a divergence-free space is performed. A noteworthy aspect of the study is that, in each incompressibility treatment, the same boundary conditions are used (and further developed) which allows a direct comparison to be made. Problems associated with implementation are also discussed and an optimal choice of the computational parameters has been proposed and verified. Numerical results show that the present state-of-the-art truly incompressible method (based on a velocity correction) suffer from density accumulation errors. To address this issue, an algorithm, based on a correction for both particle velocities and positions, is presented. The usefulness of this density correction is examined and demonstrated in the last part of the paper

Simulation of Cavity Flow by the Lattice Boltzmann Method

A detailed analysis is presented to demonstrate the capabilities of the lattice Boltzmann method. Thorough comparisons with other numerical solutions for the two-dimensional, driven cavity flow show that the lattice Boltzmann method gives accurate results over a wide range of Reynolds numbers. Studies of errors and convergence rates are carried out. Compressibility effects are quantified for different maximum velocities, and parameter ranges are found for stable simulations. The paper's objective is to stimulate further work using this relatively new approach for applied engineering problems in transport phenomena utilizing parallel computers.Comment: Submitted to J. Comput. Physics, late

A Comparative Study of an Asymptotic Preserving Scheme and Unified Gas-kinetic Scheme in Continuum Flow Limit

Asymptotic preserving (AP) schemes are targeting to simulate both continuum and rarefied flows. Many AP schemes have been developed and are capable of capturing the Euler limit in the continuum regime. However, to get accurate Navier-Stokes solutions is still challenging for many AP schemes. In order to distinguish the numerical effects of different AP schemes on the simulation results in the continuum flow limit, an implicit-explicit (IMEX) AP scheme and the unified gas kinetic scheme (UGKS) based on Bhatnagar-Gross-Krook (BGk) kinetic equation will be applied in the flow simulation in both transition and continuum flow regimes. As a benchmark test case, the lid-driven cavity flow is used for the comparison of these two AP schemes. The numerical results show that the UGKS captures the viscous solution accurately. The velocity profiles are very close to the classical benchmark solutions. However, the IMEX AP scheme seems have difficulty to get these solutions. Based on the analysis and the numerical experiments, it is realized that the dissipation of AP schemes in continuum limit is closely related to the numerical treatment of collision and transport of the kinetic equation. Numerically it becomes necessary to couple the convection and collision terms in both flux evaluation at a cell interface and the collision source term treatment inside each control volume

Automatic grid refinement criterion for lattice Boltzmann method

In all kinds of engineering problems, and in particular in methods for computational fluid dynamics based on regular grids, local grid refinement is of crucial importance. To save on computational expense, many applications require to resolve a wide range of scales present in a numerical simulation by locally adding more mesh points. In general, the need for a higher (or a lower) resolution is not known a priori, and it is therefore difficult to locate areas for which local grid refinement is required. In this paper, we propose a novel algorithm for the lattice Boltzmann method, based on physical concepts, to automatically construct a pattern of local refinement. We apply the idea to the two-dimensional lid-driven cavity and show that the automatically refined grid can lead to results of equal quality with less grid points, thus sparing computational resources and time. The proposed automatic grid refinement strategy has been implemented in the parallel open-source library Palabos