Lagrangian boundary equation and unsteady separation of elliptical cylinder at angle of attack

In this document the Lagrangian boundary equation is introduced to steady the separation of an abruptly moved elliptical cylinder at the angle of attack. Not only the occurrence of separation singular points but also their forward movement with time were calculated. The computation also revealed that the separation pattern would change from trailing edge separation to leading edge separation. In regard to the methodology of computation, a transformation was introduced to map the non-uniform mesh on the physical plane) to the uniform mesh on an auxiliary plane. Thus, it is only required to tighten the mesh (locally on the physical plane to improve the accuracy without increasing too much computing time. In addition, the advantages of the equal space finite difference, such as simplicity and high accuracy, will remain. Furthermore, a complicated variable boundary problem (separation point moving forward) was treated as a fixed boundary problem which significantly simplifies the process.