The Research For The Velocity-correction Based Immersed Boundary-lattice Boltzmann Method And Its Application

Recently, the immersed boundary method (IBM) has been developed into a popular numericaltechnique in the community of computational fluid dynamics (CFD). In addition, the latticeBoltzmann method (LBM) has gained wide range applications in recent years. Since both of them usethe Cartesian mesh, an efficient solver can be generated by combining IBM and LBM, which is calledIB-LBM. In the past time, many efforts have been made in the development and applications withIB-LBM. However, there are still some shortcomings in this newly approach. In this work, two majorimprovements were made: non-slip boundary satisfied and first-order of accuracy near the boundary.A direct velocity correction-based immersed boundary-lattice Boltzmann method (IB-LBM) ispresented in this work, which enforce the non-slip boundary condition. In the conventional IBM, thenon-slip boundary is only approximately satisfied. As a result, the streamline penetration to the solidbody occurs. To overcome this shortcoming, in the present study, the velocity at the boundary point isdirectly obtained from the non-slip boundary condition (that is, the fluid velocities at boundarypositions are equal to the boundary velocities) and then the velocity in the vicinity of the boundarypoints is modified by interpolation. To validate the proposed method, the two-dimensional (2D)stationary and moving boundary flow problems are simulation. As shown in the present numericalresults, the streamline penetration phenomenon is eliminated due to the enforcement of non-slipcondition. The obtained results compare very well with available data in the literature.To improve the computational efficiency, the non-uniform mesh is usually employed in theapplication of IB-LBM. In this work, the Taylor series expansion and least squared-based LBM(TLLBM) is used to apply IBM on the the non-uniform mesh. Due to the limitation of virtual memory,it is not easy to apply TLLBM in three-dimensional (3D) simulations. To overcome this difficulty, anefficient LBM solver based on the one-dimensional interpolation was developed. As compared toTLLBM, much less coefficients are stored. Combing with this efficient LBM solver, the new IB-LBMwas easily extended to3D simulation. The3D flows around complex stationary and movingboundaries were simulated. The obtained numerical results are agreed well with the results andfindings in the literature.