: Classically, fluid dynamics have been dealt with analytically because of the lack of numerical resources (Yeung, 1982). With the development of computational ability, many formulations have been developed which typically use the traditional Navier-Stokes equations along with an Eulerian grid. Today, there exists the possibility of using a moving grid (Lagrangian) along with a meshless discretization. The first issue in meshless fluid dynamics is the equations of motion. There are currently two types of Lagrangian formulations. Spherical Particle Hydrodynamics (SPH) is a method which calculates all equations of motion explicitly. The Moving Particle Semi-implicit (MPS) method uses a mathematical foundation based on SPH. However, instead of calculating all laws of motion explicitly, a fractional time step is performed to calculate pressure. A proposed method, Lagrange Implicit Fraction Step (LIFS), has been created which improves the mathematical formulations on the fluid domain. The LIFS method returns to Continuum mechanics to construct the laws of motion based on decomposing all forces of a volume. It is assumed that all forces on this volume can be linearly superposed to calculate the accelerations of each mass. The LIFS method calculates pressure from a boundary value problem with the inclusion of proper flux boundary conditions. The second issue in meshless Lagrangian dynamics is the calculation of derivatives across a domain. The Monte Carlo Integration (MCI) method uses weighted averages to calculate operators. However, the MCI method can be very inaccurate, and is not suitable for sparse grids. The Radial Basis Function (RBF) method is introduced and studied as a possibility to calculate meshless operators. The RBF method involves a solution of a system of equations to calculate interpolants. Machine expenses are shown to limit the viability of the RBF method for large domains.

https://calhoun.nps.edu/bitstream/10945/1724/1/05Jan_Silverberg.pdf

On Lagrangian meshless methods in free-surface flows

: The powering requirement of a ship is one of the most important aspects of naval architecture. Traditionally, ships have been tested for hull resistance using hydrodynamic tank testing. Tank testing evaluates models of ships by measuring their resistance in a tow tank. This has proved to be useful and accurate, but is very time consuming, expensive, and has inherent scaling errors. Because of these reasons, today many vessels are sold on the market without any model testing. Another set of design tools is parametric predictions. Parametric predictions contain acquired data for a specific family of hull forms and use key hull parameters to evaluate a particular design. Parametric predictions run quickly, but cannot be used to evaluate any hull outside of the limits of previously tested hulls. Computational Fluid Dynamics (CFD) codes are a much newer method of determining the powering requirement for ships. CFD uses numerical modeling to simulate the forces which act on the ship. Unlimited testing takes a fraction of the time and effort as compared to tank testing. However, it is not yet wholly proven in its accuracy. An investigation has been made using tank testing and CFD to predict the new David Pedrick Mk II Navy 44 Sail Training Crafts (STC) performance, The performance prediction process proved most accurate when using tank data to aid the CFD calculations. Using this combined method along with an aerodynamic calculation for the Mk II Navy 44 STC, a Velocity Prediction Program (VPP) was constructed. Finally, the new VPP as well as previous parametric VPPs were used to predict a full set of performance figures. These tools were also used to improve the rudder design of the Mk II Navy 44 STC.

/pdf/performance-prediction-of-the-mk-ii-navy-44-sail-training-48yryj1bg4.pdf

Performance Prediction of the Mk II Navy 44 Sail Training Craft with respect to Tank Testing, Velocity Prediction Programs, and Computational Fluid Dynamics

Jon P. Silverberg

Papers

On Lagrangian meshless methods in free-surface flows

Performance Prediction of the Mk II Navy 44 Sail Training Craft with respect to Tank Testing, Velocity Prediction Programs, and Computational Fluid Dynamics