title: Mass-conserved volumetric lattice Boltzmann method for complex flows with willfully moving boundaries.
abstract: In this paper, we develop a mass-conserved volumetric lattice Boltzmann method (MCVLBM) for numerically solving fluid dynamics with willfully moving arbitrary boundaries. In MCVLBM, fluid particles are uniformly distributed in lattice cells and the lattice Boltzmann equations deal with the time evolution of the particle distribution function. By introducing a volumetric parameter P(x,y,z,t) defined as the occupation of solid volume in the cell, we distinguish three types of lattice cells in the simulation domain: solid cell (pure solid occupation, P=1), fluid cell (pure fluid occupation, P=0), and boundary cell (partial solid and partial fluid, 0<P<1). The formulation of volumetric lattice Boltzmann equations are self-regularized through P and consist of three parts: (1) collision taking into account the momentum exchange between the willfully moving boundary and the flow; (2) streaming accompanying a volumetric bounce-back procedure in boundary cells; and (3) boundary-induced volumetric fluid migration moving the residual fluid particles into the flow domain when the boundary swipes over a boundary cell toward a solid cell. The MCVLBM strictly satisfies mass conservation and can handle irregular boundary orientation and motion with respect to the mesh. Validation studies are carried out in four cases. The first is to simulate fluid dynamics in syringes focusing on how MCVLBM captures the underlying physics of flow driven by a willfully moving piston. The second and third cases are two-dimensional (2D) peristaltic flow and three-dimensional (3D) pipe flow, respectively. In each case, we compare the MCVLBM simulation result with the analytical solution and achieve quantitatively good agreements. The fourth case is to simulate blood flow in human aortic arteries with a very complicated irregular boundary. We study steady flow in two dimensions and unsteady flow via the pulsation of the cardiac cycle in three dimensions. In the 2D case, both vector (velocity) and scalar (pressure) fields are compared to computation results from a well-established Navier-Stokes solver and reasonably good agreements are obtained. In the 3D case, the unsteady flow pattern and wall shear stress are well captured at the representative time instants during the pulsation. The validations demonstrate that the MCVLBM is a relatively simple but reliable computation scheme to deal with static or moving irregular boundaries.
authors.affiliation: Department of Mechanical Engineering, Indiana University-Purdue University Indianapolis, Indianapolis, Indiana 46202, USA.
authors.forename: Huidan
authors.initials: H
authors.lastname: Yu
authors.affiliation: Department of Mechanical Engineering, Indiana University-Purdue University Indianapolis, Indianapolis, Indiana 46202, USA.
authors.forename: Xi
authors.initials: X
authors.lastname: Chen
authors.affiliation: Department of Computer Science, Kent State University, Kent, Ohio 44240, USA.
authors.forename: Zhiqiang
authors.initials: Z
authors.lastname: Wang
authors.affiliation: Department of Mechanical Engineering, Indiana University-Purdue University Indianapolis, Indianapolis, Indiana 46202, USA.
authors.forename: Debanjan
authors.initials: D
authors.lastname: Deep
authors.affiliation: Department of Computer and Information Science, Indiana University-Purdue University Indianapolis, Indianapolis, Indiana 46202, USA.
authors.forename: Everton
authors.initials: E
authors.lastname: Lima
authors.affiliation: Department of Computer Science, Kent State University, Kent, Ohio 44240, USA.
authors.forename: Ye
authors.initials: Y
authors.lastname: Zhao
authors.affiliation: Department of Radiology and Imaging Sciences, Indiana University School of Medicine, Indianapolis, Indiana 46202, USA.
authors.forename: Shawn D
authors.initials: SD
authors.lastname: Teague
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D057446:Hydrodynamics; D008962:Models, Theoretical; D012212:Rheology / Q000379:methods*