Chapter 4 - Conservative Models

Abstract

Viable discrete models have been developed for vibrating strings, heat conduction and convection, free surface, laminar, and turbulent fluid flows, shockwave generation, elastic vibration, and evolution of planetary-type bodies. The forces in these models are always consistent with the long- and short-range forces that prevail and the modeling applies with equal ease to both linear and nonlinear phenomena. This chapter focuses on the conservative models and describes the derived physical insights and advantages of such models. The chapter presents the basic concepts of discrete conductive heat transfer by concentrating on the prototype problem of heat flow in a bar and the basic mechanisms of discrete elasticity by concentrating on the vibration of an elastic bar. As an example of a discrete conservative model for laminar and turbulent fluid flows, the chapter examines the flow of a liquid out of a nozzle.