Numerical Study of the double mach reflection using shock - capturing with sub - cell accuracy

Abstract

This thesis deals with the numerical and analytical studies of the Double Mach reflection (DMR). Double Mach reflection can occur when a shock wave encounters an obstacle. There are some unknowns when DMR is concerned. This thesis helps to make these unknowns solvable. Compressible Navier-Stokes solver (CNS) is used for performing simulations. The simulations are based on immersed boundary method (IBM) and boundary fitted method (BFM). This thesis consists of two main parts, fundamentals and numerical/analytical solutions. Firstly, literature research on fundamentals of numerical methods, shock waves and compressible flows are described. Secondly, numerical simulations of Double Mach reflection are performed on high-performance computing (HPC) system. While simulations are performed, the problems which are encountered, are explained and illuminated in detail. Simulations are compared with each other and also with the reference article [1]. In addition, simulations are analytically verified by equations from literatures. Double Mach reflection studies are mostly experimental heretofore. Hence, in this study verification of simulations by determining the location of the first and second triple points T' and T'', respectively, which are the two breaking points of the Double Mach reflection, are done newly. With literature research it is understood that without aid of simulations, the equations cannot be solved. For this reason, solving the equations using only initial conditions is terminated with failure. As a result, the values obtained from the simulations are applied to the equations and results are verified with small errors.