COMPUTATIONAL FLUID DYNAMICS THROUGH AN UNSTRUCTURED LATTICE BOLTZMANN SCHEME

摘要

Computational fluid dynamics, in its conventional meaning, computes pertinent flow fields in terms of velocity, density, pressure and temperature by numerically solving the Navier-Stokes equations in time and space. At the turn of the 1980s, the Lattice Boltzmann Method (LBM) has been proposed as an alternative approach to solve fluid dynamics problems and due to the refinements and the extensions of the last years, it has been used to successfully compute a number of nontrivial fluid dynamics problems, from incompressible turbulence to multiphase flow and bubble flow simulations. The most severe limitation of the original method is the uniform Cartesian grid on which the LBM must be constructed, that requires the approximation of a curved solid boundary by a series of stair steps. This represents a particularly severe limitation for practical engineering purposes especially when there is a need for high resolutions near the body or the walls. Among the recent advances in lattice Boltzmann research that have lead to substantial enhancement of the capabilities of the method to handle complex geometries, a particularly remarkable option is represented by changing the solution procedure from the original "stream and collide" to a finite volume technique. This paper presents a compact and efficient finite-volume lattice Boltzmann formulation on unstructured grids based on a cell-vertex scheme recently proposed in literature to integrate the differential form of the lattice Boltzmann equation. It is shown that the method tolerates significant grid distortions without showing any appreciable numerical viscosity effects at second order in the mesh size, thus allowing a time-accurate description of transitional flows. Moreover, a new set of boundary conditions to handle flows with open boundaries is presented. The resulting model has been tested against typical flow problems at low and moderate Reynolds numbers.