Introduction to finite-difference methods for numerical fluid dynamics
This work is intended to be a beginner`s exercise book for the study of basic finite-difference techniques in computational fluid dynamics. It 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 student is expected, however, to have some familiarity with the FORTRAN computer language, as the syntax of the computer codes themselves is not discussed. Topics examined in this work 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 {Kappa}-{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 codes themselves. Concepts introduced in this work 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 tensor, and the modeling of transport equations. A glossary is provided which defines these and other terms.
- Research Organization:
- Los Alamos National Lab., NM (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 212567
- Report Number(s):
- LA--12984; ON: DE96008885
- Country of Publication:
- United States
- Language:
- English
Similar Records
A computational model for viscous fluid flow, heat transfer, and melting in in situ vitrification melt pools
A computational model for viscous fluid flow, heat transfer, and melting in in situ vitrification melt pools
ZEPHYR3D: A finite difference computer program for three-dimensional, transient incompressible flow problems
Technical Report
·
Thu Oct 31 23:00:00 EST 1991
·
OSTI ID:10140275
A computational model for viscous fluid flow, heat transfer, and melting in in situ vitrification melt pools
Technical Report
·
Thu Oct 31 23:00:00 EST 1991
·
OSTI ID:5504904
ZEPHYR3D: A finite difference computer program for three-dimensional, transient incompressible flow problems
Technical Report
·
Wed May 01 00:00:00 EDT 1991
·
OSTI ID:5758546