High-Resolution TVD Schemes for the Analysis of. I. Inviscid Supersonic andTransonic Flows. II. Viscous Flows with Shock-Induced Separation and Heat Transfer

摘要

Application of TVD schemes to both inviscid and viscous flows is considered. Themathematical and physical bases of TVD schemes are discussed. First and second-order accurate TVD schemes and a second-order accurate Lax-Wendroff scheme are used to compute solutions to the Riemann problem in order to investigate the capability of each to resolve shocks, rarefactions, and contact surfaces. Second-order finite-volume and finite-difference TVD schemes are used to obtain solutions to inviscid supersonic and transonic cascade flow problems. TVD schemes are shown to be superior to the Lax-Wendroff family of schemes for both transient and steady-state computations. TVD methodology is extended to solution of viscous flow problems. A first-order time accurate, second-order space accurate algorithm is contrasted against a second-order time and space accurate algorithm for solution of the viscous Burgers' equation. Necessity of using the fully second-order accurate algorithm at low Reynolds numbers is shown. Solutions are computed to problems of laminar shock-boundary-layer interaction and unsteady, laminar, shock-induced heat transfer using the new algorithms. These algorithms provide the capability to accurately predict separation, reattachment, and pressure and skin friction profiles for shock-boundary-layer interaction. Extremely accurate comparison with theory and experiment is also evident for the unsteady shock-induced head transfer problem.