Introduction to Finite Difference Methods for Numerical Fluid Dynamics
Evan Scannapieco and Francis H. Harlow
This work grew out of a series of exercises that Frank Harlow, a senior
fellow in the Fluid Dynamics Group (T-3) at Los Alamos National
Laboratory developed to train undergraduate students in the basics
of numerical fluid dynamics. My job during my year at LANL
was rather different than his other students, as instead of using
these exercises as a launching point for further research, he and I
developed them into a self-contained textbook that could be used by students
outside of T-3.
The work is written for a student level ranging from high-school senior
to university senior. Equations are derived from basic principles using
algebra. Some discussion of partial differential equations is included,
but knowledge of calculus is not essential. The work does assume, however,
some familiarity with the FORTRAN computing language.
Topics examined include one-dimensional heat flow, one-dimensional
compressible fluid flow, two-dimensional compressible fluid flow, and
two dimensional incompressible fluid flow with additions of the
equations of heat flow and the K-epsilon model for turbulence transport.
Emphasis is placed on numerical instabilities and methods by which
they can be avoided, techniques that can be used to evaluate the accuracy of
finite-difference approximations, and the writing of the finite-difference
Concepts introduced include flux and conservation, implicit and explicit methods,
Lagrangian and Eulerian methods, shocks and rarefactions, donor-cell and
cell-centered advective fluxes, compressible and incompressible fluids,
the Boussinesq approximation for heat flow, Cartesian tensor notation, the Boussinesq
approximation for the Reynolds stress tensors, and the modelling of transport equations.
A glossary is provided that defines these and other terms.
This work was published locally as Los Alamos National Lab Report 12984
and a pdf file version is available here
(part 1) and here (part 2)
in order to make this document accessible to a wider
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Background: Painting of Santa Fe by Dr. Harlow