ME 543 Computational Fluid Dynamics (3-0-0-6)
Basic equations of Fluid Dynamics: General form of a conservation law; Equation of mass conservation; Conservation law of momentum; Conservation equation of energy. The dynamic levels of approximation. Mathematical nature of PDEs and flow equations. Basic Discretization techniques: Finite Difference Method (FDM); Analysis and Application of Numerical Schemes: Consistency; Stability; Convergence; Fourier or von Neumann stability analysis; Modified equation; Application of FDM to wave, Heat, Laplace and Burgers equations. Integration methods for systems of ODEs: Linear multi-step methods; Predictor-corrector schemes; ADI methods; The Runge-Kutta schemes. Vorticity-stream function formulation. Solution of Navier-Stokes equations using MAC algorithm. The Finite Volume Method (FVM) and conservative discretization. Numerical solution of the incompressible Navier-Stokes equations: Primitive variable formulation; Pressure correction techniques like SIMPLE, SIMPLER and SIMPLEC; Brief introduction to compressible flows and numerical schemes – quick idea of Euler equations, homogenity and flux jacobian. Introduction to upwind schemes.
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H. K. Versteeg and W. Malalasekera, An introduction to computational fluid dynamics: The finite volume method 3e, Pearson Education, 2007.
C. Hirsch, Numerical Computation of Internal and External Flows, Vol.1 and 2, John Wiley & Sons, 2007.