Thermal lattice Boltzmann flux solver and its application for simulation of incompressible thermal flows

Based on the lattice Boltzmann method (LBM), the lattice Boltzmann flux solver (LBFS), which combines the advantages of conventional Navier-Stokes solvers and lattice Boltzmann solvers, was proposed recently. Specifically, LBFS applies the finite volume method to solve the macroscopic governing equations which provide solutions for macroscopic flow variables at cell centers. In the meantime, numerical fluxes at each cell interface are evaluated by local reconstruction of LBM solution. In other words, in LBFS, LBM is only locally applied at the cell interface for one streaming step. This is quite different from the conventional LBM, which is globally applied in the whole flow domain. This paper shows three different versions of LBFS respectively for isothermal, thermal and compressible flows and their relationships with the standard LBM. In particular, the performance of isothermal LBFS in terms of accuracy, efficiency and stability is investigated by comparing it with the standard LBM. The thermal LBFS is simplified by using the D2Q4 lattice velocity model and its performance is examined by its application to simulate natural convection with high Rayleigh numbers. It is demonstrated that the compressible LBFS can be effectively used to simulate both inviscid and viscous flows by incorporating non-equilibrium effects into the process for inviscid flux reconstruction. Several numerical examples, including lid-driven cavity flow, natural convection in a square cavity at Rayleigh numbers of 10

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“…The macroscopic Navier-Stokes equations for conservation laws can be recovered by substituting Equation (7) into Equations (8) and (9) [9,10]:…”

Section: Chapman-enskog Analysismentioning

confidence: 99%

“…In Equation (11), ,  P and Q are respectively mass, momentum and energy fluxes and can be given by lattice summations of DDFs and TDFs [9,10]:…”

Section: Chapman-enskog Analysismentioning

confidence: 99%

From Lattice Boltzmann Method to Lattice Boltzmann Flux Solver

Wang

Yang

Chen

2015

Entropy

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“…Apparently, Equation (27) recovers Equation (20) exactly. In the present work, Equations (28) and (29) are, respectively, replaced by the following formulas…”

Section: Modifications On Stlbmmentioning

confidence: 99%

A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method

2017

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An unconditionally stable thermal lattice Boltzmann method (USTLBM) is proposed in this paper for simulating incompressible thermal flows. In USTLBM, solutions to the macroscopic governing equations that are recovered from lattice Boltzmann equation (LBE) through Chapman-Enskog (C-E) expansion analysis are resolved in a predictor-corrector scheme and reconstructed within lattice Boltzmann framework. The development of USTLBM is inspired by the recently proposed simplified thermal lattice Boltzmann method (STLBM). Comparing with STLBM which can only achieve the first-order of accuracy in time, the present USTLBM ensures the second-order of accuracy both in space and in time. Meanwhile, all merits of STLBM are maintained by USTLBM. Specifically, USTLBM directly updates macroscopic variables rather than distribution functions, which greatly saves virtual memories and facilitates implementation of physical boundary conditions. Through von Neumann stability analysis, it can be theoretically proven that USTLBM is unconditionally stable. It is also shown in numerical tests that, comparing to STLBM, lower numerical error can be expected in USTLBM at the same mesh resolution. Four typical numerical examples are presented to demonstrate the robustness of USTLBM and its flexibility on non-uniform and body-fitted meshes.

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“…Natural convection has been investigated by many researchers [7][8][9] . We extended it to investigate the case in a square cavity of natural convection with a suspended circle particle in viscous fluid.…”

Section: Natural Convection With a Neutrally Buoyant Particle In Viscmentioning

confidence: 99%

“…Figure 8 shows the kinetic energy in different Rayleigh numbers, which shows that when Ra=10 4 , the oscillation amplitude is greatest, which agrees well with the force and motion behavior. [7][8][9] . It is easy to found that Nu becomes greater as the increase of Ra.…”

mentioning

confidence: 99%

An Improved Momentum-Exchanged Immersed Boundary-Based Lattice Boltzmann Method for Incompressible Viscous Thermal Flows

Chen

Niu

2016

Int. J. Mod. Phys. Conf. Ser.

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An improved momentum-exchanged immersed boundary-based lattice Boltzmann method (MEIB-LBM) for incompressible viscous thermal flows is presented here. MEIB-LBM was first proposed by Niu et al 2 , which has been shown later 3,4 that the non-slip boundary condition is not satisfied. Wang. et al. 2 and Hu. et al 3 overcome this drawback by iterative method. But it needs to give an appropriate relaxation parameter. In this work, we come back to the intrinsic feature of LBM, which uses the density distribution function as a dependent variable to evolve the flow field, and uses the density distribution function correction at the neighboring Euler mesh points to satisfy the non-slip boundary condition on the immersed boundary. The same idea can also be applied to the thermal flows with fluid-structure interference. The merits of present improvements for the original MEIB-LBM are that the intrinsic feature of LBM is kept and the flow penetration across the immersed boundaries is avoided. To validate the present method, examples, including forced convection over a stationary heated circular cylinder for heat flux condition, and natural convection with a suspended circle particle in viscous fluid, are simulated. The streamlines, isothermal contours, the drag coefficients and Nusselt numbers are calculated and compared to the benchmark results to demonstrate the effective of the present method.

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Thermal lattice Boltzmann flux solver and its application for simulation of incompressible thermal flows

Cited by 86 publications

References 49 publications

From Lattice Boltzmann Method to Lattice Boltzmann Flux Solver

From Lattice Boltzmann Method to Lattice Boltzmann Flux Solver

A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method

An Improved Momentum-Exchanged Immersed Boundary-Based Lattice Boltzmann Method for Incompressible Viscous Thermal Flows

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