Hp. Langtangen et O. Munthe, Solving systems of partial differential equations using object-oriented programming techniques with coupled heat and fluid flow as example, ACM T MATH, 27(1), 2001, pp. 1-26
This paper exploits object-oriented implementation techniques to facilitate
the development of computer codes for solving systems of coupled partial d
ifferential equations. We show how to build a simulator for equation system
s by merging independent solvers for each equation that enters the system.
The main goal is to obtain a rapid, robust, and reliable software developme
nt process with extensive reuse of implemented code. Coupled heat and fluid
flow in pipes is used as example for illustrating the implementation techn
iques. We also present some results for the particular case of temperature-
dependent generalized Newtonian fluid flow between two nonconcentric cylind
ers. The general applicability of the approach is discussed.