In this work, the results obtained from the simulation of sedimentation of an elliptical cylinder in a viscous fluid are presented. The fluid flow velocity and pressure fields are evaluated by the famous lattice Boltzmann method (LBM). A smoothed profile method (SPM) is considered to enforce the no-slip boundary condition at the curved boundaries of the elliptical cylinder. The coupling between LBM LBM: Lattice Boltzmann Method and SPM SPM: Smoothed Profile Method is done by adding a hydrodynamic force term to the discretized version of the lattice Boltzmann equation. At first, the developed numerical code is validated by applying it to the unbounded laminar flow over an elliptical cylinder for different values of Reynolds number, Re. Later, simulations are carried out for sedimentation of an elliptical particle in a closed enclosure by considering different values for Re defined by terminal settling velocity of the cylinder. The robustness and accuracy of present simulation technique is assessed by comparing the particle trajectories and orientations obtained at different Re with the results from the existing literature. It is observed that, over a period of time, the particle attains steady state constant velocity and sediments horizontally when Re is low (Re=1.9) and moderate (Re=12.6). Whereas, an oscillating pattern for the sedimentation velocity is observed when Re is 32.9.

In this work, the natural convection in an annulus between two concentric cylinders is studied numerically. The fluid flow between the cylinders is solved by the lattice Boltzmann method (LBM) while a separate finite difference method (FDM) is used to solve the heat transfer. No-slip and constant boundary conditions at curved boundaries of the cylinders are treated with a smoothed profile method (SPM). At first, the velocity and temperature profiles obtained from the present LBM-SPM and FDM-SPM are validated with the corresponding theoretical results. Later, natural convection simulations inside the annulus are performed using coupled scheme of LBM-FDM-SPM by varying Ra in the range Ra=1000, Ra=10000, Ra=50000, and Ra=100000. From the temperature and fluid flow patterns obtained at different Ra, it is found that the heat transfer is mainly dominated by conduction process when Ra is low and by convection process when Ra is high.

The flow between two rotating concentric cylinders, also known as Taylor-Couette flow system, is one of the most widely studied systems in the classical fluid dynamics. In this work, a two-dimensional Taylor-Couette flow system is simulated using the lattice Boltzmann method combined with the smoothed profile method. The fluid flow between the rotating cylinders is solved by lattice Boltzmann equation while the curved boundaries of the cylinders are treated with a smoothed profile function. To assess the validity of the present simulation technique, three different cases of rotation of the cylinders were considered: ⅰ) inner cylinder is only rotating, ⅱ) outer cylinder is only rotating, and ⅲ) both inner and outer cylinders are rotating. For all the three cases, the numerical results of the flow velocity in azimuthal direction and the hydrodynamic torque acting on the cylinders are in good agreement with the corresponding analytical solution results.