A New Lagrangian Method for Time-Dependent Inviscid Flow Computation

This paper presents a new Lagrangian approach for the two-dimensional (2-D) time-dependent Euler equations. It may be considered as a sequel to the authors' previous Lagrangian approaches for steady supersonic flow computations [C. Y. Loh and W. H. Hui, J. Comput. Phys., 89 (1990), pp. 207--240; W. H. Hui and C. Y. Loh, J. Comput. Phys., 103 (1992), pp. 450--464; W. H. Hui and C. Y. Loh, J. Comput. Phys., 103 (1992), pp. 465--471; C. Y. Loh and M. S. Liou, J. Comput. Phys., 104 (1993), pp. 150--161; C. Y. Loh and M. S. Liou, SIAM J. Sci. Comput., 15 (1994), pp. 1038--1058; C. Y. Loh and M. S. Liou, J. Comput. Phys., 113 (1994), pp. 224--248]. The theoretical background and the intrinsic flow coordinates as well as the Lagrangian conservation form are introduced based on the concept of material functions (or path functions). A TVD scheme of the Godunov type is chosen to describe the numerical procedure. Several examples are then given to justify the claimed advantages of the new methodology, namely, (a) any contact discontinuities are crisply solved and (b) grids are automatically and accurately generated following pathlines.