Numerical Computation of Internal and External Flows

THE MATHEMATICAL MODELS FOR FLUID FLOW SIMULATIONS AT VARIOUS LEVELS OF APPROXIMATION: Introduction; The Basic Equations of Fluid Dynamics; The Dynamical Levels of Approximation; The Mathematical Nature of the Flow Equations and Their Boundary Conditions; BASIC DISCRETIZATION TECHNIQUES: The Finite Difference Method; The Finite Element Method; Finite Volume Method and Conservative Discretizations; THE ANALYSIS OF NUMERICAL SCHEMES: The Concepts of Consistency, Stability and Convergence; The Von Neumann Method for Stability Analysis; The Method of the Equivalent Differential Equation for the Analysis of Stability; The Matrix Method for Stability Analysis; THE RESOLUTION OF DISCRETIZED EQUATIONS: Integration Methods for Systems of Ordinary Differential Equations; Iterative Methods for the Resolution of Algebraic Systems.