Numerical Computation of Internal and External Flows Vol.1: Fundamentals of Numerical Discretization

Part -1: the Mathematical Models for Fluid Flow Simulations at Various Levels of Approximation The Basic Equations of Fluid Dynamics The Dynamic Levels of Approximation The Mathematical Nature of the Flow Equations and Their Boundary Conditions Part - 2: Basic Discretization Techniques The Finite Difference Method The Finite Element Method Finite Volume Method and Conservative Discretizations Part -3: The Analysis of Numerical Schemes The Concepts of Consistency, Stabilityand Convergence The Von Neumann Method for Stability Analysis The Methos of the Equivalent Differential Equation for the Analysis of Stability The Matrix method for Stability Analysis Part - 4: The Resolution of Discretized Equations Integration Methods for Systems of Ordinary Differential Equations Iterative Methods for the Resolution of Algebraic Systems Appendix: Thomas Algorithm for Tridiagonal Systems Index