Physical Modeling and Computational Techniques for Thermal and Fluid-dynamics [electronic resource] : Practical Numerical Mathematics / by Maurizio Bottoni.

Ordinary differential equations -- Partial differential equations and the method of characteristics -- Methods of orthogonal collocations (OC) -- Numerical methods for the solution of the convection-diffusion equation and QUICK algorithm -- Numerical solution of large linear systems -- Numerical solution of Poisson equation -- Derivation and numerical solutions of Poisson-like equations -- Numerical treatment of the transport equations of turbulence -- Formulae Synopsis -- Acronyms -- Nomenclature -- References -- Index -- Historical notes.

This book on computational techniques for thermal and fluid-dynamic problems arose from seminars given by the author at the Institute of Nuclear Energy Technology of Tsinghua University in Beijing, China. The book is composed of eight chapters-- some of which are characterized by a scholastic approach, others are devoted to numerical solution of ordinary differential equations of first order, and of partial differential equations of first and second order, respectively. In Chapter IV, basic concepts of consistency, stability and convergence of discretization algorithms are covered in some detail. Other parts of the book follow a less conventional approach, mainly informed by the author’s experience in teaching and development of computer programs. Among these is Chapter III, where the residual method of Orthogonal Collocations is presented in several variants, ranging from the classical Galerkin method to Point and Domain Collocations, applied to numerical solution of partial differential equations of first order. In most cases solutions of fluid dynamic problems are led through the discretization process, to the numerical solutions of large linear systems. Intended to impart a basic understanding of numerical techniques that would enable readers to deal with problems of Computational Fluid Dynamics at research level, the book is ideal as a reference for graduate students, researchers, and practitioners. Explains the Quadratic Upstream Interpolation for Convective Kinematics method and applies it to an algorithm for two-phase flow problems; Presents the Successive Over Relaxation theory from its rigorous theoretical viewpoint, and includes several numerical examples given in the annexed computer programs; Thoroughly reviews several methods for solving a model Poisson equation; Illustrates in detail the pressure method for obtaining a Poisson-like equation for pressure in a fluid domain; Features a full chapter dedicated to turbulence theories, detailing the numerical treatment of several transport equations, including scalar fluxes, variance of temperature fluctuations, Reynolds stresses, and dissipation of turbulent kinetic energy.