Temporal and Spatial Discretization Relationships

Abstract

For a significant number of engineering systems, by careful choice of the solution coordinate system the fluid flow structure can be made steady or steadier. The reduction of unsteadiness, may in some situations involve using several coordinate systems. This practice is common in turbomacinery design where sets of adjacent stationary and rotating blades are modelled in stationary and rotating coordinate system, respectively. Use of this approach, with a sliding grid interface, enables meaningful steady solutions to be produced which can aid design analysis. In this chapter, through considering the substantial derivative, the relationship between coordinate system choice, unsteadiness levels, and solution accuracy and economy are explored.