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One Day Lecture Series

A one day series of lectures on Finite Element Methods for Computational Fluid Dynamics is being planned for the benefit of young researchers working in this field who have participated in the Trefftz Workshop. It will be held on Thursday 19th September 2002, following the Workshop.

Details of the lectures are shown below.

The lecture series will be given by;

James F. Barbour Professor in Engineering and Chairman
Mechanical Engineering and Materials Science
Rice University, Houston, Texas

The lecture series will concern the following subjects:

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Progress and power of flow simulation and modelling (how much flow simulation and modelling progressed in recent years and how it enables us to address complex engineering problems).

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Governing equations and boundary conditions.

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Spatial discretization for advection-diffusion equations.

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Time integration and related solution techniques (stability, accuracy, nonlinear solution techniques).

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Spatial discretization for incompressible flows.

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Stabilized formulations in the context of the time-dependent advection diffusion equations.

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Computational aspects of the stabilized formulations.

Further details, including fees and possible support from the EC, will be made available on this website in due course.

Please indicate your interest in this lecture series on the Workshop Registration Form.

  

LECTURES

Finite Element Methods for Computational Fluid Dynamics 

 

08.45-09.30 1.

Progress and Power of Flow Simulation And Modeling

Two motivational lectures on how much flow simulation and modeling progressed in recent years, and how it enables us address complex engineering problems

1a Computational Mechanics in Aerospace Applications

Examples: parachute systems, space station crew return vehicle, trains, planes

1b  Computational Environmental Fluid Mechanics
Examples: free-surface flows, flow over dams, tidal flows in bays
2. Governing Equations and Boundary Conditions

A brief review of the governing equations of unsteady incompressible flows and the time-dependent advection-diffusion equation; introductory scale analysis; boundary conditions and computational boundary conditions

09.30-10.10 2a Navier-Stokes Equations of Incompressible Flows and Advection-Diffusion Equation
Understanding the momentum equation and the incompressibility constraint; stress tensor; Newtonian fluids; advection-diffusion equation
10.10-10.40 2b Scale Analysis and Boundary Conditions

Peclet and Reynolds numbers; boundary layer concept; boundary conditions; computational boundaries and boundary conditions

10.40-11.00 Short Break

 

3.  Spatial Discretization

Understanding the concept of spatial discretization for an advection-diffusion equation; how to discretize the governing equations to obtain algebraic equations or ordinary differential equations

 

11.00-11.30 3a Spatial Discretization with the Finite Difference Method

One-dimensional finite differences; multi-dimensional finite differences

 

11.30-12.20 3b Spatial Discretization with the Finite Element Method

Finite element shape (interpolation) functions; elements; test function; weighted residual formulation; global equation system; element-level vectors and matrices; assembly of the element-level vectors and matrices

 

4. Time-Integration and Related Solution Techniques

A review of time-integration in the context of finite element methods; stability and accuracy; nonlinear solution techniques; iterative solution of linear equation systems

 

12.20-13.00 4a Time-Integration Techniques

Time-integration of the ordinary differential equations obtained after spatial discretization; explicit and implicit methods; predictor/multi-corrector method

 

13.00-14.00 Lunch Break

 

14.00-14.40 4b Non-linear Solution Techniques and Iterative Solution of Linear Equations
Newton-Raphson method; iterative solution techniques for linear equation systems; how to compute the residual of the linear equation system; preconditioning; how to update the solution vector after each iteration

 

5 Spatial Discretization for Incompressible Flows

Finite element discretization of the Navier-Stokes equations of incompressible flows; weighted residual formulation; element-level vectors and matrices

 

14.40-15.10 5a Finite Element Discretization of the Navier-Stokes Equations of Incompressible Flows

Weak formulation and finite element spatial discretization; obtaining the nonlinear ordinary differential equation system corresponding to the momentum equation and the algebraic constraint equation system corresponding to the incompressibility constraint

 

15.10-15.40 5b Element-Level Vectors and Matrices for the Navier-Stokes Equations of Incompressible Flows
Derivation of the element-level vectors and matrices; element-level matrices for nonlinear terms; assembly of element-level vectors and matrices

 

15.40-16.00 Short Break

 

6 Stabilized Formulations

Understanding the stabilized formulations in the context of the time-dependent advection diffusion equation; the streamline-upwind/Petrov-Galerkin (SUPG) stabilization; extension to incompressible flows; pressure-stabilizing/Petrov-Galerkin (PSPG) formulation; Galerkin/least-squares (GLS) formulation

 

16.00-16.30 6a Stabilized Formulation for the Advection-Diffusion Equation

Element Peclet number; element Reynolds number; SUPG stabilization in 1D; stabilization parameter; SUPG stabilization in 2D and 3D

 

16.30-17.00 6b Stabilized Formulation for the Navier-Stokes Equations
SUPG stabilization; PSPG stabilization; GLS stabilization and its relationship to SUPG and PSPG stabilizations

 

7 Computational Aspects of the Stabilized Formulations

The nonlinear ordinary differential equation system corresponding to the momentum equation and the algebraic constraint equation corresponding to the incompressibility constraint; derivation of the element-level vectors and matrices

 

17.00-17.30 7a Semi-Discrete Forms Corresponding to the Stabilized Formulations
Semi-discrete forms; derivation of the element-level vectors; simplifications

 

7b Fully Discrete Forms Corresponding to the Stabilized Formulations

Time-discretization; derivation of the element-level matrices; simplifications

 

 

 

Copyright 2001.
For problems or questions regarding this web contact [S.E.Adam@ex.ac.ukl].