No abstract

Numerous methods and procedures have preceded successful modeling of flow in physical domains of complex geometry by the lattice Boltzmann method (LBM). Common to these methods is partial deviation from the basic structure of the LBM, resulting in deterioration of accuracy, stability, simplicity and ease of application. In order to minimize the drawbacks as much as possible, a form of LBM based on the principles of the classical CFD with complete transformation of the 2D equations of flow in curvilinear coordinates is proposed in. Suitable forms of the local equilibrium distribution function and of the force term have been developed for the corresponding set of equations, which has been solved by the standard LBM using the original form of the boundary conditions. In order to eliminate the drawbacks of this approach coming from the use of finite difference method in modeling some of the terms, an improved method is outlined as follows. The transformed set of equations of 2D flow-including the Navier-Stokes equations and the shallow water equations-is introduced in a form in which all terms are compatible with the basic structure of the LBM. This results in higher accuracy, while the simple structure of the method and its efficiency is maintained. The benefits of the proposed approach are demonstrated by three test examples. The results of the proposed method are compared with the analytical solution, with results obtained by a laboratory model and with the results of other numerical methods.