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In this study, a new upwind scheme has been used to solve the continuous Boltzmann equation and to develop its application in the effective solution of incompressible flows. Time derivative in the Boltzmann equation has been discretized using the first-order forward finite difference scheme. The spatial derivatives in the Boltzmann equation have been discretized using this new scheme. Further, the combined effects of the upwind differential mechanism along with the finite difference method are presented to enhancement the stability of the standard lattice Boltzmann method in solving problems with high Reynolds numbers. To confirm the validation of the proposed method, one unsteady problem, this has an analytical solution, and two incompressible steady problems which have not analytical solutions, have been solved numerically. The first benchmark problem is the conductive heat transfer on a slab and two last problems are flow over a flat plate and flow in a lid-driven cavity. In order to check the numerical accuracy and stability of the proposed method, the results have been compared with the standard lattice Boltzmann method and the finite difference lattice Boltzmann method. The proposed method guarantees that without applying the filtering method, more stable and accurate results are obtained compared with the finite difference lattice Boltzmann method. The simulation results show the effectiveness of the present method and its appropriate compatibility with analytical solutions and other numerical methods. [ABSTRACT FROM AUTHOR]

In this study, an alternative numerical method is proposed to predict the two-phase flow during dendritic growth under melt convection. It consists of two main parts. The phase-field method (PFM) is used for modeling the solid phase and tracking the morphological changes during dendritic solidification, and the finite-difference lattice Boltzmann method (FDLBM) is used for predicting the fluid flow of the liquid phase. The no-slip boundary condition to take into account the interaction between liquid and solid phases at the interface is modeled as a diffusive drag force. This method is referred to as phase field-finite difference lattice Boltzmann method (PF-FDLBM). In the numerical formulation, a collision term with single relaxation time (SRT) is used for simplicity, and a negative viscosity term is included to improve numerical stability. The proposed method can be implemented on regular and non-regular grids. Two-dimensional benchmark computations of flows past a circular cylinder show that the no-slip boundary condition is well satisfied. The flow patterns and drag coefficients are appropriately predicted even for flows at low Reynolds numbers, in which viscous forces commonly deteriorate numerical stability. Then, simulations of dendritic growth under melt convection are carried out with the present method. The effect of melt convection on the solidification patterns is well predicted for an alloy with its actual physical properties. Finally, the efficiency of the proposed method is evaluated considering an increase of the relaxation time, and its influence related to the computational resources. As a result, faster and stable computations are possible by appropriately setting the relaxation time and the negative viscosity term in PF-FDLBM formulation. [ABSTRACT FROM AUTHOR]

Summary: Fluid‐structure interactions (FSI) of rigid and flexible bodies are simulated in this article. For the fluid flow, multidirect forcing immersed boundary method (IBM) is adopted to capture the moving boundary, and lattice Boltzmann method (LBM) is used to evolve the flow field. Compared with our previous no‐penetration IBM, less iterations are required in this work. In addition, larger velocity in lattice units can be used and the nonphysical force oscillations are suppressed due to the C3 6‐point kernel. Multi‐relaxation‐time collision operator and local grid refinement are also adopted in LBM to enhance the numerical stability and efficiency. To improve the efficiency of the FSI coupling algorithm, the mesh of the deformable structure can be coarser than the Lagrangian mesh using Newton‐Cotes formulas to integrate the traction on the structure surface. A variety of benchmarks, including flow around a circular cylinder with Reynold number ranging from 20 to 200, forced oscillation of a circular cylinder, vortex‐induced vibration (VIV) of an elastically mounted circular cylinder in two degrees of freedom, and VIV of an elastic cantilever beam attached to a circular cylinder, are carried out to evaluate the accuracy and stability of the present coupling algorithm. For the benchmark FSI problem considered in this article, a reduction of 54% of the calculation time is achieved using coarser structure mesh. As an application of the FSI coupling algorithm, the mechanism of an elastic beam in the wake of a circular cylinder is discussed. [ABSTRACT FROM AUTHOR]

Immersed boundary-lattice Boltzmann methods (IB-LBM) with the single-relaxation time (SRT) cause non-physical distortion in fluid velocity when the Reynolds number is low, i.e. the relaxation time τ is high, and IB-LBM requires high spatial resolution to stably simulate high Reynolds number flows. An immersed boundary-finite difference lattice Boltzmann method (IB-FDLBM) using two-relaxation times (TRT) is therefore proposed in this study to simulate low and high Reynolds number flows stably and accurately. Benchmark problems such as circular Couette flows, flows past a circular cylinder and a sphere at various Reynolds numbers are carried out for validation. The main conclusions obtained are as follows: (1) TRT reduces numerical errors causing non-physical distortion in the fluid velocity at low Reynolds numbers, and accurate predictions are obtained when the parameter Λ, which is a function of the two relaxation times, is low, (2) for stable simulation the parameter Λ should be decreased as the Reynolds number increases, (3) implementation of TRT and the implicit direct forcing method into IB-FDLBM can solve two problems in simulation of low Reynolds number flows, i.e. non-physical velocity distortion and non-physical penetration of flow into the solid body, and (4) IB-FDLBM with TRT gives good predictions of the drag coefficients of a circular cylinder and a sphere in uniform flows for a wide range of the Reynolds number, Re, i.e., 0.1 ≤ Re ≤ 1x104.

The main steam stop valve (MSV) in thermal or nuclear power plants is liable to undergo excitation by sound having a specific frequency. The purposes of this article are to clarify the mechanism of the sound generation in the MSV using numerical analysis and to propose a suppression method for the sound generation. The analysis results were validated experimentally using a 1/5-scale model of a typical MSV. The analysis results showed good agreement with the experimental data. From the analysis results, it was clarified that the sound of the MSV was generated by the hole-tone in the opening and the acoustic resonance in the vertical direction of the MSV. A method was proposed to install triangular or slanted tabs at the inlet seat of the MSV in order to prevent formation of vortex rings in the opening which leads to the hole-tone. Effects of the proposed method were tested experimentally. Eight triangular tabs having a height of 15% of the inner diameter in the seat reduced the peak value of the sound pressure by 60%. Eight slanted tabs having a height of 7.5% of the inner diameter in the seat suppressed generation of the hole-tone in the MSV. These results showed that the slanted tabs are effective in suppression of the hole-tone compared with the triangular tabs.

An immersed boundary method based on a finite difference lattice Boltzmann method (IB-FDLBM) is presented. The FDLBM solves the discrete Boltzmann equation including an additional collision term by using finite difference schemes. The additional term works as a negative viscosity in the macroscopic level and allows us to alter the fluid viscosity while keeping the other relevant parameters of the simulation fixed. The immersed boundary method employs a direct-forcing method, which utilizes external forces at Lagrangian points embedded on immersed boundaries to impose the no-slip boundary condition. Several benchmark simulations are carried out to validate the developed method, i.e., flows past a circular cylinder, a falling particle, and interaction between two falling particles. Couette flows between a stationary and a rotating cylinder are also simulated at various values of the relaxation time for collision. The main conclusions obtained are as follows: (1) steady flows past a stationary circular cylinder are well predicted, (2) the motions of particles falling through liquids predicted using IB-FDLBM quantitatively agree well with those obtained using immersed boundary methods based on the lattice Boltzmann equation (IB-LBM), (3) the developed method well predicts the interaction between two particles falling through a liquid, e.g., the drafting-kissing-tumbling motion, and (4) distortion of velocity fields in circular Couette flows at high relaxation times is removed by the additional collision term.

An improved finite difference lattice Boltzmann method (FDLBM) is developed to simulate incompressible flows. The basic idea is to decrease the density fluctuation which might lead to compressible error in the flows with high pressure gradient or high speed motion. The equation of state is modified by including the attractive and repulsive forces between particles to adjust the compressibility of fluid. This effect is incorporated by applying acceleration modification which is deduced based on macroscopic dynamics. Using this method the sound speed of the fluid can be also controlled easily. Numerical simulations of steady Poiseuille flow and unsteady Womersley flow were adopted to validate our model. The results show that the proposed model is much more efficient than the conventional LBGK method when solving the incompressible flows with high pressure gradient.

In this study, the immersed boundary-finite difference lattice Boltzmann method (IB-FDLBM) using the feedback momentum forcing scheme is proposed and implemented to simulate 2-D incompressible flows. IB-FBLBM incorporates the immersed boundary method (IBM) into the finite difference lattice Boltzmann method (FDLBM) devised to alleviate shortcomings by using the uniform Cartesian grid of the standard lattice Boltzmann method (LBM). In order to obtain numerical stability while combining IBM with FDLBM, this method utilizes feedback momentum forcing scheme and equilibrium velocity approach to take into account the change of momentum induced by a body force on the immersed boundaries. This approach has the advantages of being simple and easy to implement, and does not require modification of the original governing equations. In order to confirm the applicability and validation of IB-FDLBM, the lid-driven cavity flow with a circular cylinder, the external steady flows around a circular cylinder and external steady flows around a circular cylinder near a plane wall are simulated with a range of Reynolds numbers. The current numerical results are consistent with those of existing researches. [ABSTRACT FROM AUTHOR]

The applicability of the immersed boundary-finite difference lattice Boltzmann method (IB-FDLBM) to high Reynolds number flows about a circular cylinder is examined. Two-dimensional simulations of flows past a stationary circular cylinder are carried out for a wide range of the Reynolds number, Re, i.e., 1 ≤ Re ≤ 1×105. An immersed boundary-lattice Boltzmann method (IB-LBM) is also used for comparison. Then free-falling circular cylinders are simulated to demonstrate the feasibility of predicting moving particles at high Reynolds numbers. The main conclusions obtained are as follows: (1) steady and unsteady flows about a stationary cylinder are well predicted with IB-LBM and IB-FDLBM, provided that the spatial resolution is high enough to satisfy the conditions of numerical stability, (2) high spatial resolution is required for stable IB-LBM simulation of high Reynolds number flows, (3) IB-FDLBM can stably simulate flows at very high Reynolds numbers without increasing the spatial resolution, (4) IB-FDLBM gives reasonable predictions of the drag coefficient for 1 ≤ Re ≤ 1×105, and (5) IB-FDLBM gives accurate predictions for the motion of free-falling cylinders at intermediate Reynolds numbers. [ABSTRACT FROM AUTHOR]

Abstract: With the advent of state-of-the-art computers and their rapid availability, the time is ripe for the development of efficient uncertainty quantification (UQ) methods to reduce the complexity of numerical models used to simulate complicated systems with incomplete knowledge and data. The spectral stochastic finite element method (SSFEM) which is one of the widely used UQ methods, regards uncertainty as generating a new dimension and the solution as dependent on this dimension. A convergent expansion along the new dimension is then sought in terms of the polynomial chaos system, and the coefficients in this representation are determined through a Galerkin approach. This approach provides an accurate representation even when only a small number of terms are used in the spectral expansion; consequently, saving in computational resource can be realized compared to the Monte Carlo (MC) scheme. Recent development of a finite difference lattice Boltzmann method (FDLBM) that provides a convenient algorithm for setting the boundary condition allows the flow of Newtonian and non-Newtonian fluids, with and without external body forces to be simulated with ease. Also, the inherent compressibility effect in the conventional lattice Boltzmann method, which might produce significant errors in some incompressible flow simulations, is eliminated. As such, the FDLBM together with an efficient UQ method can be used to treat incompressible flows with built in uncertainty, such as blood flow in stenosed arteries. The objective of this paper is to develop a stochastic numerical solver for steady incompressible viscous flows by combining the FDLBM with a SSFEM. Validation against MC solutions of channel/Couette, driven cavity, and sudden expansion flows are carried out. [Copyright &y& Elsevier]

Abstract: The sound and underwater sound emitted from a water drop colliding with a water surface are simulated by a new model of the finite difference lattice Boltzmann method. The two-particle immiscible fluid model is modified to simulate sound in the gas phase and underwater simultaneously. In the very early stage after the collision, sounds propagating into the gas and liquid phases are successively detected, and the effects of drop shape and gas bubbles are also observed. [Copyright &y& Elsevier]

new beadless disperser, an ultra-thin film high-shear disperser (UFHD), was developed, and the flow in its dispersion part (a flow between rotating and stationary rings) was simulated using the finite difference lattice Boltzmann method (FDLBM). The efficiency of the FDLBM for this kind of flow field was verified. The FDLBM possesses some distinctive features such as relatively easy implementation of boundary conditions in complicated geometries, high efficiency in parallel processing, and flexible reproduction of the interface between multiple phases, that make the method very suitable for simulating complex flows in the disperser, in which the fluid consists of a mixture of solvent and particles, and the deformation, breakup and coalescence of suspended particles occur. It was shown that the performance of the disperser can easily be simulated and elucidated by the FDLBM. [ABSTRACT FROM AUTHOR]

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The lattice Boltzman method ( LBM) and the finite difference-based lattice Boltzmann method ( FDLBM) are quite recent approaches for simulating fluid flow, which have been proven as valid and efficient tools in a variety of complex flow problems. They are considered attractive alternatives to conventional finite-difference schemes because they recover the Navier-Stokes equations and are computationally more stable, and easily parallelizable. However, most models of the LBM or FDLBM are for incompressible fluids because of the simplicity of the structure of the model. Although some models for compressible thermal fluids have been introduced, these models are for monatomic gases, and suffer from the instability in calculations. A lattice BGK model based on a finite difference scheme with an internal degree of freedom is employed and it is shown that a diatomic gas such as air is successfully simulated. In this research we present a 2-dimensional edge tone to predict the frequency characteristics of discrete oscillations of a jet-edge feedback cycle by the FDLBM in which any specific heat ratio γ can be chosen freely. The jet is chosen long enough in order to guarantee the parabolic velocity profile of a jet at the outlet, and the edge is of an angle of α=23°. At a stand-off distance w, the edge is inserted along the centerline of the jet, and a sinuous instability wave with real frequency is assumed to be created in the vicinity of the nozzle exit and to propagate towards the downstream. We have succeeded in capturing very small pressure fluctuations resulting from periodic oscillation of the jet around the edge. [ABSTRACT FROM AUTHOR]

The shock wave process represents an abrupt change in fluid properties, in which finite variations in pressure, temperature, and density occur over the shock thickness which is comparable to the mean free path of the gas molecules involved. This shock wave fluid phenomenon is simulated by using the finite difference lattice Boltzmann method (FDLBM). In this paper, a new model is proposed using the lattice BGK compressible fluid model in FDLBM for the purpose of speeding up the calculation as well as stabilizing the numerical scheme. The numerical results of the proposed model show good agreement with the theoretical predictions. [ABSTRACT FROM AUTHOR]

We analyze the numerical stability of Finite Difference Lattice Boltzmann Method (FDLBM) by means of von Neumann stability analysis. The stability boundary of the FDLBM depends on the BGK relaxation time, the CFL number, the mean flow velocity, and the wavenumber. As the BGK relaxation time is increased at constant CFL number, the stability of the central difference LB scheme may not be ensured. The limits of maximum stable velocity are obtained around 0.39, 0.43, and 0.43 for the central difference, for the explicit upwind difference, and for the semi-implicit upwind difference schemes, respectively. We derive artificial viscosities for every difference scheme and investigate their influence on numerical stability. The requirements for artificial viscosity is consistent with the conditions derived from von Neumann stability analysis. This analysis elucidates that the upwind difference schemes are suitable for simulation of high Reynolds number flows. [ABSTRACT FROM AUTHOR]