The application of computational fluid dynamics to the modelling and design of high-speed boats

Computational fluid dynamics solvers were applied to the field of high-speed boat design. The lattice Boltzmann method was used to assess the water-phase of the flow around a number of high-speed hullform geometries, and was validated against empirical industry and literature data. A heave dynamics capability was developed to assess the heave equilibrium position of a high speed boat, showing close agreement with industry data. A mesh movement and evolutionary optimisation software was applied to the aero-dynamic optimisation of a high-speed catamaran using a Reynolds-averaged Navier-Stokes solver for modelling of the air phase of the flow

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 moving control volume approach to computing hydrodynamic forces and torques on immersed bodies

We present a moving control volume (CV) approach to computing hydrodynamic forces and torques on complex geometries. The method requires surface and volumetric integrals over a simple and regular Cartesian box that moves with an arbitrary velocity to enclose the body at all times. The moving box is aligned with Cartesian grid faces, which makes the integral evaluation straightforward in an immersed boundary (IB) framework. Discontinuous and noisy derivatives of velocity and pressure at the fluid-structure interface are avoided and far-field (smooth) velocity and pressure information is used. We re-visit the approach to compute hydrodynamic forces and torques through force/torque balance equation in a Lagrangian frame that some of us took in a prior work (Bhalla et al., J Comp Phys, 2013). We prove the equivalence of the two approaches for IB methods, thanks to the use of Peskin's delta functions. Both approaches are able to suppress spurious force oscillations and are in excellent agreement, as expected theoretically. Test cases ranging from Stokes to high Reynolds number regimes are considered. We discuss regridding issues for the moving CV method in an adaptive mesh refinement (AMR) context. The proposed moving CV method is not limited to a specific IB method and can also be used, for example, with embedded boundary methods

High-order interpolation between adjacent cartesian finite difference grids of different size

Nested cartesian grid systems by design require interpolation of solution fields from coarser to finer grid systems. While several choices are available, preserving accuracy, stability and efficiency at the same time require careful design of the interpolation schemes. Given this context, a series of interpolation algorithms for nested cartesian finite difference grids of different size were developed and tested. These algorithms are based on post-processing, on each local grid, the raw (bi/trilinear) information passed to the halo points from coarser grids. In this way modularity is maximized while preserving locality. The results obtained indicate that the schemes improve markedly the convergence rates and the overall accuracy of finite difference codes with varying grid sizes.Publicado en: Mecánica Computacional vol. XXXV, no. 15Facultad de Ingenierí