A Fully Implicit Finite Volume Lattice Boltzmann Method for Turbulent Flows

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.

Integrating a Stabilized Radial Basis Function Method with Lattice Boltzmann Method

“…Furthermore, they require recalculations of the collision for each refinement level. To avoid this, a second approach is used, which uncouples the time and space increments and uses conventional computational fluid dynamic (CFD) methods such as the finitevolume method (FVM) [17][18][19][20][21][22], the finite-difference method (FDM) [23][24][25][26][27][28][29][30][31][32][33][34], the finiteelement method (FEM) [35][36][37][38][39][40][41], or the meshless method [42][43][44][45]. This approach suffers from numerical diffusion, which leads to dissipation error in proportion to the mesh distribution.…”