Numerical Techniques in Electromagnetics is designed to show the reader how to pose, numerically analyze, and solve electromagnetic (EM) problems. It gives them the ability to expand their problem-solving skills using a variety of available numerical methods. Topics covered include fundamental concepts in EM; numerical methods; finite difference methods; variational methods, including moment methods and finite element methods; transmission-line matrix or modeling (TLM); and Monte Carlo methods. The simplicity of presentation of topics throughout the book makes this an ideal text for teaching or self-study by senior undergraduates, graduate students, and practicing engineers.

Numerical Techniques in Electromagnetics, Second Edition

Introduction Overview of problems and approaches Model test and similarity laws Full scale tests Numerical approaches (Computational Fluid Dynamics) Basic equations, Basic techniques Applications. Propeller Flows: Propeller geometry and other basics, Propeller curves Numerical methods for propeller design Lifting line theory Lifting surface theory BEM for propellers Field methods Cavitation Experimental approach Propeller design procedure. Resistance and propulsion: Resistance and propulsion concepts Interaction between ship and propeller Decomposition of resistance Experimental approach Towing tanks and experimental set up Resistance test Method ITTC 1957 Method of Hughes-Prohaska Propulsion test Additional resistance under service conditions Simple design approaches CFD approaches for steady flow Wave resistance computations Viscous flow computations Problems for fast and unconventional ships. Ship Seakeeping: Introduction to seakeeping Experimental approaches (model and full-scale) Waves and seaway Airy waves (harmonic waves of small amplitude) Natural seaway Wind and seaway Wave climate Numerical prediction of ship seakeeping Overview of computational methods Strip method Rankine panel methods Problems for fast and unconventional ships Further quantities in regular waves Ship responses in stationary seaway Simulation methods Long-term distributions Slamming. Manoeuvring: Simulation of manoeuvring with known coefficients Coordinate systems and definitions Body forces and manoeuvring motions Linear motion equations CFD for manoeuvring Experimental approaches Manoeuvring tests for full-scale ships in sea trials Model tests Rudders Computation of body forces Slender-body theory Influence of heel Shallow-water effect Jet thrusters Stop manoeuvres. Boundary element methods: Green function formulation Integral equations Source elements Point source Regular first-order panel Jensen panel Higher-order panel Vortex elements Dipole elements Point dipole. Numerical examples for BEM: Two-dimensional body in infinite flow Theory Numerical implementation.

Practical Ship Hydrodynamics

The formulation of a general numerical method for two-dimensional incompressible flow and heat transfer in irregular-shaped domains is presented. The calculation domain is first divided into six-node macroelements. Then each macroelement is divided into four three-node triangular subelements. Polygonal control volumes are associated with the nodes of these elements. All dependent variables other than pressure are stored at the nodes of the subelements, and they are interpolated by functions that respond appropriately to an element Peclet number and the direction of an element-averaged velocity vector. The pressure is stored only at the vertices of the macroelements and is interpolated linearly in these elements. The discretization equations are obtained by deriving algebraic approximations to integral conservation equations applied to the polygonal control volumes. An iterative procedure akin to SIMPLER is used to solve the discretization equations.

A control volume finite-element method for two-dimensional fluid flow and heat transfer

A novel computational procedure for the prediction of incompressible fluid flow using primitive variables is presented. The formulation retains the geometric flexibility of the finite-element method and derives the governing discrete algebraic equations by using a conservation balance applied to discrete control volumes distributed throughout the domain. A novel method of closure, to relate the control volume surface values to the nodal point values, is introduced whereby a local discrete analog to the governing differential equation is formed at the control volume Surfaces. From this discrete equation analog the control surface values are determined in terms of the nodal values that represent the discrete problem unknowns. The manner in which this discrete equation is formed, solved, and used permits resolution of two longstanding problems in computational fluid dynamics, namely accurate convection modeling and preclusion of pressure field decoupling. A new and general boundary condition specifi...

Control Volume Finite-Element Method for Heat Transfer and Fluid Flow Using Colocated Variables— 1. Computational Procedure

A control volume-based finite-element method for solving the Navier-Stokes equations using equal-order velocity-pressure interpolation is presented. Unlike the unequal-order-type methods that compute pressure at much fewer grid points than velocity, the proposed equal-order method calculates velocity and pressure at all the grid points in the domain. The validity of the method is established by applying it to solve some test problems

G. F. Carey

Papers

Finite element analysis in fluid dynamics