A generalised lattice Boltzmann method with block-structured adaptive mesh refinement

The Lattice Boltzmann method (LBM) is a relatively new development in computational fluid dynamics (CFD). Instead of approximating the Navier-Stokes equations, the approach is based on solving a simplified version of the Boltzmann equation on a specific discrete space. It can be shown via a Chapman Enskog expansion that for vanishing Knudsen number the LBM recovers the Navier-Stokes equations. The standard LBM is limited to equally spaced Cartesian grids, making this approach notably expensive for capturing thin boundary layers, and therefore impractical for most relevant problems in aerodynamics. In this work, conventional numerical methods are implemented to solve the two-dimensional discrete-velocity Boltzmann equation in generalised curvilinear coordinates to simulate fluid flows with non-Cartesian grids. Several test cases are used for verification and validation, and the results have been extensively compared with the available numerical and experimental literature with very favourable outcome confirming the feasibility of the implemented methodology. The generalised LBM resolves large gradients in the wall vicinity with fewer mesh elements than the Cartesian LBM; therefore, it substantially reduces the computational effort. Flows over the 2D circular cylinder and the NACA0012 aerofoil are specifically investigated to assess the accuracy and performance of this approach for external aerodynamics. Moreover, the generalised LBM has been implemented into AMROC (Adaptive Mesh Refinement in Object-oriented C++) software infrastructure, a fully parallelised finite-volume framework that uses a block-structured adaptive mesh refinement. This development is a new class of LBM scheme with block-structured adaptive mesh refinement on curvilinear grids. The latest is implemented with the mapped mesh strategy, and various test cases are solved for validation, including heat transfer flows. Overall, this project enhanced the current capabilities of the standard LBM by combining the generalised LBM with AMROC capabilities