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Proceedings ArticleDOI

Improving resolution of three-dimensional lattice boltzmann simulations using bicubic spline interpolation for moving boundaries

About: The article was published on 2020-01-06. It has received 1 citations till now. The article focuses on the topics: Interpolation & Lattice Boltzmann methods.
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Journal ArticleDOI
TL;DR: In this paper , proper orthogonal decomposition (POD)-ROM LBM in the general form, presented an appropriate matrix form for the LBM as explained, and implemented POD or DEIM on that matrix form.
Abstract: Recently, the reduced order model (ROM) has been applied to reduce the computational cost of numerical methods. Merging this approach with the lattice Boltzmann method (LBM) as a powerful mesoscale fluid solver seems promising. Dealing with this idea requires a matrix form for the LBM. This matrix form must represent all the LBM's algorithm steps (including boundary condition implementation) to just one specific matrix-vector relation. Furthermore, the LBM contains some nonlinear parts inside the equilibrium distribution function (EDF), which must be treated with a nonlinear ROM like the discrete empirical interpolation method (DEIM). So, in this paper, we discuss proper orthogonal decomposition (POD)-ROM LBM in the general form, present an appropriate matrix form for the LBM as explained, and implement POD or DEIM on that matrix form. In the end, the ability of this scheme is challenged with solving the urban air pollutant transition problem over some canyons areas as a practical problem.

2 citations

References
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Journal ArticleDOI
TL;DR: In this paper, a kinetic theory approach to collision processes in ionized and neutral gases is presented, which is adequate for the unified treatment of the dynamic properties of gases over a continuous range of pressures from the Knudsen limit to the high pressure limit where the aerodynamic equations are valid.
Abstract: A kinetic theory approach to collision processes in ionized and neutral gases is presented. This approach is adequate for the unified treatment of the dynamic properties of gases over a continuous range of pressures from the Knudsen limit to the high-pressure limit where the aerodynamic equations are valid. It is also possible to satisfy the correct microscopic boundary conditions. The method consists in altering the collision terms in the Boltzmann equation. The modified collision terms are constructed so that each collision conserves particle number, momentum, and energy; other characteristics such as persistence of velocities and angular dependence may be included. The present article illustrates the technique for a simple model involving the assumption of a collision time independent of velocity; this model is applied to the study of small amplitude oscillations of one-component ionized and neutral gases. The initial value problem for unbounded space is solved by performing a Fourier transformation on the space variables and a Laplace transformation on the time variable. For uncharged gases there results the correct adiabatic limiting law for sound-wave propagation at high pressures and, in addition, one obtains a theory of absorption and dispersion of sound for arbitrary pressures. For ionized gases the difference in the nature of the organization in the low-pressure plasma oscillations and in high-pressure sound-type oscillations is studied. Two important cases are distinguished. If the wavelengths of the oscillations are long compared to either the Debye length or the mean free path, a small change in frequency is obtained as the collision frequency varies from zero to infinity. The accompanying absorption is small; it reaches its maximum value when the collision frequency equals the plasma frequency. The second case refers to waves shorter than both the Debye length and the mean free path; these waves are characterized by a very heavy absorption.

6,627 citations

Journal ArticleDOI
TL;DR: An overview of the lattice Boltzmann method, a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities, is presented.
Abstract: We present an overview of the lattice Boltzmann method (LBM), a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities. The LBM is especially useful for modeling complicated boundary conditions and multiphase interfaces. Recent extensions of this method are described, including simulations of fluid turbulence, suspension flows, and reaction diffusion systems.

6,565 citations

01 Jan 1954
TL;DR: In this article, a kinetic theory approach to collision processes in ionized and neutral gases is presented, which is adequate for the unified treatment of the dynamic properties of gases over a continuous range of pressures from the Knudsen limit to the high pressure limit where the aerodynamic equations are valid.
Abstract: A kinetic theory approach to collision processes in ionized and neutral gases is presented. This approach is adequate for the unified treatment of the dynamic properties of gases over a continuous range of pressures from the Knudsen limit to the high-pressure limit where the aerodynamic equations are valid. It is also possible to satisfy the correct microscopic boundary conditions. The method consists in altering the collision terms in the Boltzmann equation. The modified collision terms are constructed so that each collision conserves particle number, momentum, and energy; other characteristics such as persistence of velocities and angular dependence may be included. The present article illustrates the technique for a simple model involving the assumption of a collision time independent of velocity; this model is applied to the study of small amplitude oscillations of one-component ionized and neutral gases. The initial value problem for unbounded space is solved by performing a Fourier transformation on the space variables and a Laplace transformation on the time variable. For uncharged gases there results the correct adiabatic limiting law for sound-wave propagation at high pressures and, in addition, one obtains a theory of absorption and dispersion of sound for arbitrary pressures. For ionized gases the difference in the nature of the organization in the low-pressure plasma oscillations and in high-pressure sound-type oscillations is studied. Two important cases are distinguished. If the wavelengths of the oscillations are long compared to either the Debye length or the mean free path, a small change in frequency is obtained as the collision frequency varies from zero to infinity. The accompanying absorption is small; it reaches its maximum value when the collision frequency equals the plasma frequency. The second case refers to waves shorter than both the Debye length and the mean free path; these waves are characterized by a very heavy absorption.

6,004 citations

Journal ArticleDOI
01 Feb 1992-EPL
TL;DR: In this article, the Navier-Stokes equation is obtained from the kinetic BGK equation at the second-order approximation with a properly chosen equilibrium distribution, with a relaxation parameter that influences the stability of the new scheme.
Abstract: We propose the lattice BGK models, as an alternative to lattice gases or the lattice Boltzmann equation, to obtain an efficient numerical scheme for the simulation of fluid dynamics. With a properly chosen equilibrium distribution, the Navier-Stokes equation is obtained from the kinetic BGK equation at the second-order of approximation. Compared to lattice gases, the present model is noise-free, has Galileian invariance and a velocity-independent pressure. It involves a relaxation parameter that influences the stability of the new scheme. Numerical simulations are shown to confirm the speed of sound and the shear viscosity.

4,481 citations

Journal ArticleDOI
TL;DR: In this paper, Chen et al. used the half-way wall bounceback boundary condition for the 2-D Poiseuille flow with forcing to obtain second-order accuracy for the 3-D square duct flow.
Abstract: Pressure (density) and velocity boundary conditions inside a flow domain are studied for 2-D and 3-D lattice Boltzmann BGK models (LBGK) and a new method to specify these conditions are proposed. These conditions are constructed in consistency of the wall boundary condition based on an idea of bounceback of non-equilibrium distribution. When these conditions are used together with the improved incompressible LBGK model by Zou et al., the simulation results recover the analytical solution of the plane Poiseuille flow driven by pressure (density) difference with machine accuracy. Since the half-way wall bounceback boundary condition is very easy to implement and was shown theoretically to give second-order accuracy for the 2-D Poiseuille flow with forcing, it is used with pressure (density) inlet/outlet conditions proposed in this paper and in Chen et al. to study the 2-D Poiseuille flow and the 3-D square duct flow. The numerical results are approximately second-order accurate. The magnitude of the error of the half-way wall bounceback is comparable with that using some other published boundary conditions. Besides, the bounceback condition has a much better stability behavior than that of other boundary conditions.

2,001 citations