HIGHER-ORDER-ACCURATE UPWIND SCHEMES FOR SOLVING THE COMPRESSIBLE EULER AND NAVIER-STOKES EQUATIONS

A fifth-order compact upwind TVD scheme and a fourth-order compact MUS CL TVD scheme are proposed for solving the compressible Euler and Navi er Stokes equations. The fundamental form of the present schemes is ba sed on the second(third)-order-accurate upwind scheme. One of the dist inctive points using the present MUSCL TVD scheme is the ability to ca pture the discontinuities, such as slip lines or contact surfaces as w ell as shocks, more sharply th an the existing TVD scheme with a simpl er algorithm than the so-called ENO scheme. The algorithms are relativ ely simple and the formulas are quite compact. They can be applied eas ily to the existing Euler and Navier Stokes solvers based on the secon d(third)-order upwind scheme. Finally, we show some numerical results of steady and unsteady flows, including shocks, weak discontinuities a nd vortices, and the superiority of the present scheme is confirmed by comparison with the results of the ordinary numerical scheme.