Immersed Boundary Methods in the Lattice Boltzmann Equation for Flow Simulation

In this dissertation, we explore direct-forcing immersed boundary methods (IBM) under the framework of the lattice Boltzmann method (LBM), which is called the direct-forcing immersed boundary-lattice Boltzmann method (IB-LBM). First, we derive the direct-forcing formula based on the split-forcing lattice Boltzmann equation, which recovers the Navier-Stokes equation with second-order accuracy and enables us to develop a simple and accurate formula due to its kinetic nature. Then, we assess the various interface schemes under the derived direct-forcing formula. We consider not only diffuse interface schemes but also a sharp interface scheme. All tested schemes show a second-order overall accuracy. In the simulation of stationary complex boundary flows, we can observe that the sharper the interface scheme is, the more accurate the results are. The interface schemes are also applied to moving boundary problems. The sharp interface scheme shows better accuracy than the diffuse interface schemes but generates spurious oscillation in the boundary forcing terms due to the discontinuous change of nodes for the interpolation. In contrast, the diffuse interface schemes show smooth change in the boundary forcing terms but less accurate results because of discrete delta functions. Hence, the diffuse interface scheme with a corrected radius can be adopted to obtain both accurate and smooth results. Finally, a direct-forcing immersed boundary method (IBM) for the thermal lattice Boltzmann method (TLBM) is proposed to simulate non-isothermal flows. The direct-forcing IBM formulas for thermal equations are derived based on two TLBM models: a double-population model with a simplified thermal lattice Boltzmann equation (Model 1) and a hybrid model with an advection-diffusion equation of temperature (Model 2). The proposed methods are validated through natural convection problems with stationary and moving boundaries. In terms of accuracy, the results obtained from the IBMs based on both models are comparable and show a good agreement with those from other numerical methods. In contrast, the IBM based on Model 2 is more numerically efficient than the IBM based on Model 1. Overall, this study serves to establish the feasibility of the direct-forcing IB-LBM as a viable tool for computing various complex and/or moving boundary flow problems

A conservative coupling algorithm between a compressible flow and a rigid body using an Embedded Boundary method

This paper deals with a new solid-fluid coupling algorithm between a rigid body and an unsteady compressible fluid flow, using an Embedded Boundary method. The coupling with a rigid body is a first step towards the coupling with a Discrete Element method. The flow is computed using a Finite Volume approach on a Cartesian grid. The expression of numerical fluxes does not affect the general coupling algorithm and we use a one-step high-order scheme proposed by Daru and Tenaud [Daru V,Tenaud C., J. Comput. Phys. 2004]. The Embedded Boundary method is used to integrate the presence of a solid boundary in the fluid. The coupling algorithm is totally explicit and ensures exact mass conservation and a balance of momentum and energy between the fluid and the solid. It is shown that the scheme preserves uniform movement of both fluid and solid and introduces no numerical boundary roughness. The effciency of the method is demonstrated on challenging one- and two-dimensional benchmarks

A conservative and consistent implicit Cartesian cut-cell method for moving geometries with reduced spurious pressure oscillations

A conservative and consistent three-dimensional Cartesian cut-cell method is presented for reducing the spurious pressure oscillations often observed in moving body simulations in sharp-interface Cartesian grid methods. By analysing the potential sources of the oscillation in the cut-cell framework, an improved moving body algorithm is proposed for the cut-cell method for the temporal discontinuity of the solid volume change. Strict conservation of mass and momentum for both fluid and cut cells is enforced through pressure-velocity coupling to reduce local mass conservation errors. A consistent mass and momentum flux computation is employed in the finite volume method. In contrary to the commonly cut-cell methods, an implicit time integration scheme is employed in the present method, which prevents numerical instability without any additional small cut-cell treatment. The effectiveness of the present cut-cell method for reducing spurious pressure oscillations is demonstrated by simulating various two- and three-dimensional benchmark cases (in-line and transversely oscillating cylinder, oscillating and free-falling sphere), with good agreement with previous experimental measurements and other numerical methods available in the literature