Artificial boundary conditions in the Lattice Boltzmann method / vorgelegt von Daniel Heubes, geboren in Haan. Wuppertal, Februar 2017
Inhalt
- Contents
- List of figures
- Abbreviations
- Notation
- List of symbols
- 1 Introduction
- 2 Fluid dynamics and the lattice Boltzmann method
- 2.1 Modeling fluid flows
- 2.2 Boltzmann equation and its macroscopic limit
- 2.2.1 Moments of the single particle distribution
- 2.2.2 Moments of the Boltzmann equation
- 2.2.3 Alternative collision model
- 2.3 Lattice Boltzmann method
- 2.3.1 Characteristic curves
- 2.3.2 Integration of the kinetic model along its characteristics
- 2.3.3 Analytical derivation of the D3Q19 velocity set
- 2.3.4 Lattice Boltzmann equation
- 2.4 Lattice Boltzmann beyond Navier-Stokes equations
- 2.5 Problem formulation
- 3 Non-reflecting boundary conditions
- 3.1 An ideal transparent boundary condition
- 3.2 Artificial boundary conditions
- 3.3 Characteristic boundary conditions
- 3.3.1 Basic systems of characteristic boundary conditions
- 3.3.2 Characteristic analysis
- 3.3.3 Solution of the CBC system
- 3.3.4 Determination of boundary populations
- 3.4 Enhanced characteristic boundary conditions
- 4 Exact discrete artificial boundary condition for linear collision model
- 4.1 Evolution represented with digraphs
- 4.1.1 Domain of dependence
- 4.1.2 Lattice Boltzmann equation with reversed perspective
- 4.1.3 Visualization by digraphs
- 4.2 Weighted digraphs for linear collision models
- 4.3 Construction principle of the exact discrete artificial boundary condition
- 4.4 Exact discrete artificial boundary condition
- 5 Discrete artificial boundary conditions (DABCs)
- 5.1 One-dimensional DABCs for a linear collision model
- 5.1.1 Decreasing node weights
- 5.1.2 Approximate discrete artificial boundary condition
- 5.1.3 Proof of node weights' general decrease
- 5.2 Interpretation as subproblems
- 5.3 One-dimensional DABCs for a nonlinear collision model
- 5.4 General discrete artificial boundary conditions in any dimension
- 5.5 Analysis of the discrete artificial boundary conditions
- 6 Numerical results
- 6.1 Terminology
- 6.2 Approximate DABCs for linear collision models
- 6.3 One-dimensional pressure wave
- 6.4 Visual interpretation of discrete artificial boundary conditions
- 6.5 An isolated vorticity wave
- 6.6 Plane waves with different angles of incidence
- 6.7 3D square duct flow past an obstacle
- 7 Conclusions and outlook
- A Alternative discrete velocity models
- B Matrices for characteristic boundary conditions
- C Completion of the proof of Lemma 4
- D Optimal selection for expanding the domain of convergence
- E Additional numerical results
- References