WEIGHTED UPWINDING COMPACT SCHEME FOR SHOCK CAPTURING
Abstract
The Weighted Upwinding Compact Scheme in this dissertation has been constructed due to dissipation and dispersion analysis at each stencil. The new scheme is applied to many one-dimensional typical problems involving discontinuities and shock waves, and it maintains a 7th order of accuracy in smooth areas. Additionally, when using the technology of decoupling the system of WUCS, the global dependency problem of the compact scheme is transferred to a local dependency problem in shock regions. As a result of the decoupling method, the shocks are captured sharply with fewer points compared to the related schemes. Furthermore, high order, high resolution, and non-oscillation are achieved.
In future work, there will be an effort to apply the new scheme to the 2-D and 3-D Navier-Stokes equations and to multi-dimensional flows with shock-turbulence interaction.