Introduction

A beginner in the field of computing is hardly aware of the importance of formulations responsible for the accuracy in scientific computing. In theoretical fluid mechanics it is not important as to which form of Navier–Stokes equation is solved. But, in computing this is paramount, and there is always ongoing debate among practitioners about the superiority of different formulations and numerical methods employed by different schools of thought.

Governing differential equations are obtained by considering a control volume and balancing fluxes of quantities of interest, obtained in the limit of vanishing size of the control volume. This provides a point-by-point description of intrinsic properties of interest. In many methods of computing, this point description of conservation principle is integrated over a finite control volume. Obtaining governing differential equation is described in this way here, for the conservation of mass, momentum and energy. This is followed by discussion on desirability of casting differential equations in conservation form, which is found to be impervious to details of discretization to a great extent, as compared to non-conservation form.

Here, we also note that often one requires to investigate the problem by formulating the governing equation in non-inertial frame. Readers will have no difficulty in appreciating the need for it in weather forecasting. It is also appropriate and convenient for many engineering flows, where one part of the body is in relative motion with respect to other parts, as in problems of aeroelasticity. This is also needed for rigid bodies of arbitrary shape executing time-dependent motion.