A second order Shock-Adaptive Godunov-type scheme for solving the steady Euler equations in Orthogonal Lagrangian formulation has been developed and applied to compute steady supersonic and hyvpersonic flow problems. Similar to the both New Lagrangian formulation and Generalized Lagrangian formulation, the Orthogonal Lagrangian formulation employs the streamlines as coordinate lines that can inherits all advantages in the two former Lagrangian formulations; the crisp resolution of the slipline, shock resolution increasing by increasing mach number and no grid generation. Besides, the λ-coordinate is chosen to be orthogonal to the streamline axis which can minimize the well-posedness condition; M 1. Together with the application of Shock-Adaptive scheme and the condition of conservation...[ Read more ]

A second order Shock-Adaptive Godunov-type scheme for solving the steady Euler equations in Orthogonal Lagrangian formulation has been developed and applied to compute steady supersonic and hyvpersonic flow problems. Similar to the both New Lagrangian formulation and Generalized Lagrangian formulation, the Orthogonal Lagrangian formulation employs the streamlines as coordinate lines that can inherits all advantages in the two former Lagrangian formulations; the crisp resolution of the slipline, shock resolution increasing by increasing mach number and no grid generation. Besides, the λ-coordinate is chosen to be orthogonal to the streamline axis which can minimize the well-posedness condition; M > 1. Together with the application of Shock-Adaptive scheme and the condition of conservation of entropy in smooth flow, the shock can be solved in infinite order of accuracy and the overshoot near the isolat, ed slipline is successfully eliminated. Various numerical examples for supersonic flow involving strong discontinuities are given in this thesis.