Volume 22, Issue 2
A Fully Implicit Finite Volume Lattice Boltzmann Method for Turbulent Flows

Fatih Cevik & Kahraman Albayrak

Commun. Comput. Phys., 22 (2017), pp. 393-421.

Published online: 2018-04

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  • Abstract

Almost all schemes existed in the literature to solve the Lattice Boltzmann Equation like stream & collide, finite difference, finite element, finite volume schemes are explicit. However, it is known fact that implicit methods utilizes better stability and faster convergence compared to the explicit methods. In this paper, a method named herein as Implicit Finite Volume Lattice Boltzmann Method (IFVLBM) for incompressible laminar and turbulent flows is proposed and it is applied to some 2D benchmark test cases given in the literature. Alternating Direction Implicit, an approximate factorization method is used to solve the obtained algebraic system. The proposed method presents a very good agreement for all the validation cases with the literature data. The proposed method shows good stability characteristics, the CFL number is eased. IFVLBM has about 2 times faster convergence rate compared with Implicit-Explicit Runge Kutta method even though it possesses a computational burden from the solution of algebraic systems of equations.

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@Article{CiCP-22-393, author = {}, title = {A Fully Implicit Finite Volume Lattice Boltzmann Method for Turbulent Flows}, journal = {Communications in Computational Physics}, year = {2018}, volume = {22}, number = {2}, pages = {393--421}, abstract = {

Almost all schemes existed in the literature to solve the Lattice Boltzmann Equation like stream & collide, finite difference, finite element, finite volume schemes are explicit. However, it is known fact that implicit methods utilizes better stability and faster convergence compared to the explicit methods. In this paper, a method named herein as Implicit Finite Volume Lattice Boltzmann Method (IFVLBM) for incompressible laminar and turbulent flows is proposed and it is applied to some 2D benchmark test cases given in the literature. Alternating Direction Implicit, an approximate factorization method is used to solve the obtained algebraic system. The proposed method presents a very good agreement for all the validation cases with the literature data. The proposed method shows good stability characteristics, the CFL number is eased. IFVLBM has about 2 times faster convergence rate compared with Implicit-Explicit Runge Kutta method even though it possesses a computational burden from the solution of algebraic systems of equations.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0014}, url = {http://global-sci.org/intro/article_detail/cicp/11303.html} }
TY - JOUR T1 - A Fully Implicit Finite Volume Lattice Boltzmann Method for Turbulent Flows JO - Communications in Computational Physics VL - 2 SP - 393 EP - 421 PY - 2018 DA - 2018/04 SN - 22 DO - http://doi.org/10.4208/cicp.OA-2016-0014 UR - https://global-sci.org/intro/article_detail/cicp/11303.html KW - AB -

Almost all schemes existed in the literature to solve the Lattice Boltzmann Equation like stream & collide, finite difference, finite element, finite volume schemes are explicit. However, it is known fact that implicit methods utilizes better stability and faster convergence compared to the explicit methods. In this paper, a method named herein as Implicit Finite Volume Lattice Boltzmann Method (IFVLBM) for incompressible laminar and turbulent flows is proposed and it is applied to some 2D benchmark test cases given in the literature. Alternating Direction Implicit, an approximate factorization method is used to solve the obtained algebraic system. The proposed method presents a very good agreement for all the validation cases with the literature data. The proposed method shows good stability characteristics, the CFL number is eased. IFVLBM has about 2 times faster convergence rate compared with Implicit-Explicit Runge Kutta method even though it possesses a computational burden from the solution of algebraic systems of equations.

Fatih Cevik & Kahraman Albayrak. (2020). A Fully Implicit Finite Volume Lattice Boltzmann Method for Turbulent Flows. Communications in Computational Physics. 22 (2). 393-421. doi:10.4208/cicp.OA-2016-0014
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