Abstract
This study is aimed at developing a novel computational framework that seamlessly incorporates the feedback forcing model and adaptive mesh refinement mesh refinement (AMR) techniques in the immersed-boundary (IB) lattice Boltzmann method (LBM) approach, so that challenging problems, including the interactions between flowing fluids and moving objects, can be numerically investigated. Owing to the feedback forcing based IB model, the advantages, such as simple mechanics principle, explicit interpolations, and inherent satisfaction of no-slip boundary condition for solid surfaces are fully exhibited. Additionally, the "bubble' function is employed in the local mesh refinement process, so that the solution of second order accuracy at newly generated nodes can be obtained only by the spatial interpolation but no temporal interpolation. Focusing on both steady and unsteady flow around a single cylinder and bi-cylinders, a number of test cases performed in this study have demonstrated the usefulness and effectiveness of the present AMR IB-LBM approach.
Highlights
Tremendous efforts on the theoretical, computational, and experimental fronts of this subject have been made for a long history towards more and better understanding of fluid dynamics, great challenges still remain in this research area
In the study of computational fluid dynamics (CFD), despite fast development of digital computer technologies, numerical solutions with high accuracy are difficult to achieve for many engineering problems, which requires the conventional numerical methods to be enhanced by novel computational strategies
The adaptive mesh refinement (AMR)-immersed boundary (IB)-lattice Boltzmann method (LBM) model presented in this study may render the LBM approach more efficient in simulating complex fluid flow problems arising from engineering applications
Summary
As an important branch of the physics subject, fluid dynamics studies the fluid flow behaviors that take place in many aspects of the real world. In the study of computational fluid dynamics (CFD), despite fast development of digital computer technologies, numerical solutions with high accuracy are difficult to achieve for many engineering problems, which requires the conventional numerical methods to be enhanced by novel computational strategies. From the viewpoint of fluid motion description, existing CFD methods can be divided into three categories: macroscopic method, microscopic method, and mesoscopic method. The conventional methods, such as finite-difference method (FDM), finite-volume method (FVM), finite-element method (FEM), and spectral method, belong to the macroscopic category as they all assume the fluid as a continuum. When using a macroscopic method to deal with fluid dynamics problems, the governing equations are discretized into algebraic equations, which are to be numerically solved to obtain discrete solutions on the computational domain. The mesoscopic method inherits the nuggets of both macroscopic and microscopic methods, such as using less assumptions and neglecting the movement details of each single particle
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