Steady-State Solution of the Euler Equations for Transonic Flow

Abstract

The most important requirement for aeronautical applications of computational methods in fluid dynamics is the capability to predict the steady flow past a proposed configuration, so that key performance parameters such as the lift to drag ratio can be estimated. Thus, the aerodynamic design is based on analysis of steady flow. It is important to be able to calculate steady solutions of aerodynamic flows in the transonic range, where the formation of shock waves leads to the onset of drag rise, and a drastic deterioration of the lift to drag ratio as the speed of the airplane approaches the speed of sound. As the Mach number is increased and the shock waves become strong enough to produce appreciable amounts of entropy and vorticity, the assumption of potential flow becomes progressively less acceptable. The chapter also discusses time stepping schemes. The objective of the time-stepping procedure is to advance the solution to a steady state as rapidly as possible for a given amount of computational effort. The use of an implicit scheme permits a larger time step but requires more effort per time step.