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 a uthors previous Lagrangian approaches for steady supersonic flow computatio ns [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 a nd 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 ow coordinates as well as the Lagrangian conservation form a re introduced based on the concept of material functions ( or path function s). A TVD scheme of the Godunov type is chosen to describe the numerical pr ocedure. 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.