A Numerical Analysis of Flow using Streamline Coordinates : The Case of Two-dimensional Steady Incompressible Flow

Basic equations for a fluid motion are derived using streamline coordinates (φ, ψ). Streamlines are taken as the coordinate curves of φ, and the coordinate curves of ψ are so chosen that they are orthogonal with the streamlines. The quantity φ is related to the length s of the streamline by ∂φ/∂s = λ, where λ is a new variable. The quantity ψ is related to the length n of the orthogonal curve by ∂ψ/∂n = q, where q is flow velocity. A two-dimensional liquid jet from a channel with parallel walls into the atmosphere is taken as an example of numerical calculation. The basic equations are transformed into difference equations. The flow field is solved numerically, and this method is proved to be useful, especially in the case where the flow has free surfaces. There is also an important merit that the basic equations can be considerably simplified when a general picture of streamlines is predicted in advance.