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Finite Volume Discrete Boltzmann Method on a Cell-Centered Triangular Unstructured Mesh

Chen, Leitao (2016) Finite Volume Discrete Boltzmann Method on a Cell-Centered Triangular Unstructured Mesh. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Due to its basis in kinetics, the lattice Boltzmann method (LBM) has been shown to be superior to conventional computational fluid dynamic (CFD) tools that solve the Navier-Stokes (NS) equation for complex flow problems, such as multiphase and/or multicomponent flows. However, after development for decades, the LBM still has not gained prominence over other CFD tools for a number of reasons, one of which is its unsatisfactory ability to handle complex boundary geometries. The goal of the current work is to overcome this difficulty.

In order to fully integrate the unstructured mesh for treating complex boundary geometries, the discrete Boltzmann equation (DBE), which is the Eulerian counterpart of the lattice Boltzmann equation (LBE), is chosen for the study. The finite volume (FV) method is selected to solve the governing equation due to its outstanding performance in handling an unstructured mesh and its built-in conservation. Therefore, the method in the current work is called the finite volume discrete Boltzmann method (FVDBM).

A FVDBM platform, both for isothermal and thermal models, is developed in the current work, which consists of three parts: the cell-centered (CC) triangular unstructured mesh, the FVDBM solver, and the boundary treatment, among which the latter two are the main areas of contribution. In the FVDBM solver, there are three components: the time marching scheme, the flux scheme, and the collision calculator.

The flux schemes are the major area of study because of their significance in the overall FVDBM model (they control the spatial order of accuracy) and their complexity (they calculate the spatial gradient term) on the unstructured mesh. A universal stencil is developed on the arbitrary CC triangular unstructured mesh, with which two categories of flux schemes are developed systematically: the Godunov type and the non-Godunov type. As a result, a total of five schemes (three Godunov schemes and two non-Godunov schemes) with different orders of accuracy are formulated, numerically validated and analyzed. Two major conclusions can be drawn. First, for any flux scheme, Godunov or non-Godunov, its actual order is roughly one order lower than its theoretical order for velocity solutions, due to the diffusion error introduced by the unstructured mesh and the Eulerian nature of the solver. Second, a Godunov scheme is less diffusive and more stable than a non-Godunov one if they are of the same order of accuracy.

Furthermore, a unique three-step boundary treatment is developed in detail for the current model. With the proposed boundary treatment, a variety of physical boundary conditions (velocity, density, and temperature, etc.) can be realized on the complex boundaries with the triangular unstructured mesh in a unified way. It can also incorporate different lattice models indiscriminately. With sufficient numerical testing, it is found that the boundary treatment is at least second-order accurate in space, and it can accurately preserve Dirichlet boundary conditions up to machine accuracy under different scenarios.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Chen, Leitaolec67@pitt.eduLEC670000-0001-7761-5503
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairSchaefer,
Committee MemberKimber,
Committee MemberLee,
Committee MemberNeilan,
Date: 20 September 2016
Date Type: Publication
Defense Date: 23 June 2016
Approval Date: 20 September 2016
Submission Date: 15 June 2016
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 159
Institution: University of Pittsburgh
Schools and Programs: Swanson School of Engineering > Mechanical Engineering
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: lattice Boltzmann; BGK collision; finite volume method; flux schemes; order of accuracy; numerical viscosity; unstructured mesh; boundary treatment; Dirichlet Boundary
Date Deposited: 20 Sep 2016 19:22
Last Modified: 15 Nov 2016 14:33


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