Modeling of diffusion processes: Numerical solutions to the diffusion equation

Conference · Fri Jan 01 04:00:00 EST 1988

OSTI ID:6857758

Romig, Jr, A D; Pehlivanturk, N Y; Inal, O T

Many phenomena in materials science are controlled by volume diffusion. To model these phenomena it is often necessary to solve the diffusion equation under initial and boundary conditions for which analytical solutions do not exist. Specific examples requiring numerical solutions include cases where the initial composition profile is neither constant nor a simple error function, where the boundary compositions are constant nor a simple error function, where the boundary compositions are not fixed and vary as impingement occurs, and where diffusion occurs under non-iosthermal conditions. Several numerical algorithms have been used to solve these problems including explicit finite differences, implicit finite differences (Crank-Nicholson), method of lines, and finite elements. The advantages and disadvantages of each technique will be described. In a tutorial fashion, a simple fixed boundary diffusion problem and a two-phase moving boundary problem will be solved analytically and numerically and the results compared. A more complex example of a diffusion problem requiring a numerical solution will also be given. 34 refs., 11 figs., 1 tab.

• Research Organization: Sandia National Labs., Albuquerque, NM (USA)
• DOE Contract Number: AC04-76DP00789
• OSTI ID: 6857758
• Report Number(s): SAND-88-0980C; CONF-880901-13; ON: DE89003401
• Country of Publication: United States
• Language: English

Related Subjects

657000* -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990220 -- Computers
Computerized Models
& Computer Programs-- (1987-1989)
ALGORITHMS
BOUNDARY CONDITIONS
COMPUTER ARCHITECTURE
COMPUTER CODES
DIFFERENTIAL EQUATIONS
DIFFUSION
EQUATIONS
FINITE ELEMENT METHOD
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS