Desde: 06-09-1999
Hasta: 08-09-1999
Lugar: Southamptom, Reino Unido


Introduction to Finite Difference and
Finite Volume Methods
in Heat Transfer

6 - 8 September 1999
Ashurst, Southampton, UK


To develop the basics of finite difference and finite volume methods
for computational heat transfer and apply these methods to modelling
heat conduction and incompressible fluid flow and heat transfer.


Professor A. Kassab

Professor Alain Kassab, PhD., Associate Professor, Mechanical,
Aerospace and Materials Engineering Department, University of Central
Florida, USA.


DAY 1:  6th September 1999

r    Introductory remarks.  Why  numerical methods?  Classification
of numerical methods.

r    Partial differential equations of fluid mechanics and heat
transfer.  Classification, boundary conditions, and well-posed

r    Basics of finite difference methods.  Spacial discretization:
Taylor series and point collocation, control volume formulation,
finite volume formulation, and compact differencing.  Temporal
discretization:  CTCS Richardson method. FTCS explicit method, BTCS
implicit method, Crank Nicholson, Runge Kutta methods.  The Thomas
algorithm for tri-diagonal equations.

r    Stability analysis:  discrete perturbation method,
Fourier/Von-Neumann method, matrix stability analysis, and modified
equation.  The Courant Frederich Levy (CFL) and other stability

DAY 2:  7th September 1999

r    Analysis of truncation error:  dissipative error, conservative
property, dispersion error, transportive error, aliasing and
anisotropy.  Effects on spatial resolution from differencing
convective and diffusive terms.

r    Methods for transient multidimensional problems:  fractional
steps, ADI, and approximate factorization.

r    Matrix methods for steady state problems.  Norms and
conditioning number.  Direct methods:  Thomas algorithm,
Gauss-elimination, and LU decomposition.  Iterative methods:  Jacobi
iteration, Gauss-Seidel, SOR, method of lines, Multigrid methods and
minimization techniques.

r    Applications to model equations: diffusion equation, Laplace
equation, and Burgers equation.  First, second and higher order
upwinding.  The QUICK scheme and its derivatives.

DAY 3:  8th September 1999

r     Methods for Incompressible fluid flow and heat transfer:
vorticity-stream function derived variable approach, and the SIMPLE
family pressure correction algorithms.

r     Transformation of the governing equations to body-fitted
coordinate system, conservative and non-conservative formulations.
Example of the equivalence of finite volume and finite body-fitted
difference control volume formulations in 2-D heat conduction.

r     Grid generation method.  Algebraic grid generation methods:
some explicit transformation equations for grid control, Lagrange
transfinite interpolations methods, and Hermite transfinite
interpolation methods.  Partial differential equation.


Clare Bridle
Wessex Institute of Technology
Ashurst Lodge, Ashurst
Southampton, SO40 7AA
Tel:  44 (0) 238 029 3233
Fax:  44 (0) 238 029 2853

Web Site at
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