The purpose of this paper is twofold. Firstly, to present a detailedaccount of the generalized Lagrangian formulation of Hui and Zhao, in whichthe stream function and Lagrangian distance , are used asindependent variables, and secondly to assess and compare the performance ofvarious flux limiters in this formulation with their correspondingperformance in the Eulerian formulation. The generalized Lagrangianformulation is obtained by a transformation from the cartesiancoordinates x, y to the Lagrangian coordinates, . In this manner, the number of independent variablesfor steady, 3D flow is reduced from four to three, placing thisformulation on the same footing as the Eulerian formulation even for steadyflows as opposed to the conventional Lagrangian formulation whichapparently still requires four independent variables even for steadyflows. The generalized Lagrangian formulation with the Godunov schemeusing flux limiters appears to have distinct advantages over thecorresponding Eulerian formulation, particularly with respect to accuracy.Furthermore, the method requires no grid generation.
International Journal of Numerical Methods for Heat & Fluid Flow – Emerald Publishing
Published: Feb 1, 1995