KT Scheme For Several Typical Models In Fluid Mechanics

KT scheme is a high-resolution central scheme.This scheme can evaluate the wide of Riemann fan by using more precise information of the local propagation speeds.This scheme realizes the approximate solution in terms of its cell averages integrated over the Riemann fans of varying size.The major advantage of KT scheme is its simplicity-no Riemann solvers are involved.At the same time,it has small numerical viscosity,high stability and great shock-capturing ability.KT scheme is applied to numerical simulations of shock tube problems and double Mach reflection problem.It is the first simulation of double Mach reflection problem by using this scheme.It is found that KT scheme works better than others as regards the resolution of the waves appearing in the solutions.The results illustrate the theoretical support of KT scheme.In this thesis,it discusses from five parts.The main contents and the research status are introduced in Chapter 1.In Chapter 2,shock tube problems,double Mach reflection problem and its governing equations are introduced.In Chapter 3,KT scheme is described in detail,Runge-Kutta method that are employed for the time discretization and computational conditions are discussed.In Chapter 4 the results of shock tube problems and double-Mach reflection problem are analyzed,respectively.Finally,conclusions are drawn and future research is discussed.