﻿ Center of Advanced Study in Theoretical Sciences(CASTS)

A Mini-Course on Computational Fluid Dynamics

 A Mini Course: Fundamentals of Computational Fluid & Thermal Engineering by Prof. Ching-Long Lin (University of Iowa) Description: Governing equation and models of fluid flow and heat transfer; basic numerical techniques for solution; estimation of accuracy and stability of the numerical approximations Learning Objectives: 1.The student will have an understanding of fundamental governing equations of computational fluid flow and heat transfer. 2.The student will learn about basic numerical methods and analyses. Outlines: 1.Governing Equations 2.Basic Aspects of Discretization, Numerical Errors and Stability Specific Topics: 1.Introduction •What is computational fluid dynamics (CFD)? •Direct numerical simulation (DNS), large-eddy simulation (LES), and Reynolds-Averaged Navier-Stokes equation (RANS) 2.The Governing Equations of Fluid Dynamics •4 models of the flow: integral/differential, conservation/non-conservation •Substantial derivative and divergence of velocity field •Continuity equation for four different models •Momentum equation and Energy equation •Tensor notation •Strong conservation vs. weak conservation •Flux variables vs. primitive variables (conservation vs. non-conservation) 3.Simplified Mathematical Models •Euler equation •Incompressible N-S equation: criterion, decoupling from energy equation •Boussinesq approximation •Segregated vs coupled approaches •RANS: k-ε model and k-ω model •Large-eddy Simulation 4.Basics of the Numerics •Introduction: finite difference and finite volume •Taylor Table and Concept of Upwind Scheme •Explicit and Implicit Approach •Errors and Stability Analysis Numerical Methods for the Simulation of Incompressible Viscous Flow: An Introduction By Prof. Tsorng-Whay Pan (University of Houston) The Navier-Stokes equations have been known for more than a century and they still provide the most commonly used mathematical model to describe and study the motion of viscous fluids, including phenomena as complicated as turbulent flow. One can only marvel at the fact that these equations accurately describe phenomena whose length scales (resp., time scale) range from fractions of a millimeter (resp., of a second) to thousands of kilometers (resp., several years). Indeed, the Navier-Stokes equations have been validated by numerous comparisons between analytical or computational results and experimental measurements. These notes do not have the pretension to cover the full field of finite element methods for the Navier--Stokes equations; they are organized in sections as follows: 1. The Navier-Stokes equations for incompressible viscous flow. 2. Some operator splitting methods for initial value problems and applications to the Navier-Stokes equations 3. Iterative solution of the wave-like equation method for the advection subproblems 4. Iterative solution of the Stokes type subproblems. 5. Finite element approximation of the Navier-Stokes equations. 6. Numerical results
Time: 09:00 - 17:00, Tuesday,Wednesday, December 19 - 20, 2017
Room: 308, Mathematics Research Center Building (ori. New Math. Bldg.)
Speakers: Ching-Long Lin  ( Department of Mechanical and Industrial Engineering, University of Iowa, USA )
Tsorng-Whay Pan  ( University of Houston, USA )
Organizer: Chien-Cheng Chang  ( Institute of Applied Mechanics, National Taiwan University )