Ebook Fluid mechanics (4th edition): Part 2

(BQ) Part 2 book "Fluid mechanics" has contents: Computational fluid dynamics, instability, turbulence, geophysical fluid dynamics, aerodynamics, introduction to biofluid mechanics. | Chapter 11 Computational Fluid Dynamics by Howard H. Hu University of Pennsylvania Philadelphia, PA, USA 1. Introduction . . . . . . . . . . . . . . . . . . . . . 411 2. Finite Difference Method . . . . . . . . . 413 Approximation to Derivatives . . . . 413 Discretization and Its Accuracy. . . 414 Convergence, Consistency, and Stability . . . . . . . . . . . . . . . . . . . . . . 415 3. Finite Element Method . . . . . . . . . . . 418 Weak or Variational Form of Partial Differential Equations . . . . . . . . . 418 Galerkin’s Approximation and Finite Element Interpolations . . 420 Matrix Equations, Comparison with Finite Difference Method. . 421 Element Point of View of the Finite Element Method . . . . . . . . 424 4. Incompressible Viscous Fluid Flow 426 Convection-Dominated Problems. . . . . . . . . . . . . . . . . . . . . . 427 Incompressibility Condition . . . . . . Explicit MacCormack Scheme . . . . MAC Scheme . . . . . . . . . . . . . . . . . . . . -Scheme . . . . . . . . . . . . . . . . . . . . . . . Mixed Finite Element Formulation. . . . . . . . . . . . . . . . . . . 5. Three Examples . . . . . . . . . . . . . . . . . Explicit MacCormack Scheme for Driven Cavity Flow Problem . . . Explicit MacCormack Scheme for Flow Over a Square Block . . . . . Finite Element Formulation for Flow Over a Cylinder Confined in a Channel . . . . . . . . . . . . . . . . . . 6. Concluding Remarks . . . . . . . . . . . . . Exercises . . . . . . . . . . . . . . . . . . . . . . . . Literature Cited . . . . . . . . . . . . . . . . . . 429 430 433 437 438 440 440 444 450 461 463 464 1. Introduction Computational Fluid Dynamics (CFD) is a science that, with the help of digital computers, produces quantitative predictions of fluid-flow phenomena based on those conservation laws (conservation of mass, momentum, and energy) governing fluid motion. These predictions normally occur under those conditions defined in terms of flow geometry, the physical properties of a fluid, and the boundary .