A study of reference-plane methods for unsteady plane flows

The paper investigates the reference-plane method, by which an unsteady plane flow problem can be reduced to a two-dimensional one. The original version of Moretti and Abbett (1966), in which a vertical plane is chosen as reference plane, is reviewed. To follow somewhat closer the physics of the flow, a sloping reference plane containing the streamline along the wall is considered. For Ringleb flow, a local polar coordinate system is chosen. Testing consisted of calculating the change in time of the flow variables at a point downstream on the wall streamline after one application of algorithms involving (1) interpolating the values to second order from exact nodal values and (2) use of exact Ringleb values. Both vertical and sloping reference planes were used, and several different mesh sizes were tried. The errors were determined, and it was found that the equations for the sloping reference plane are less sensitive to interpolation errors.