Compact-reconstruction Weighted Essentially Non-oscillatory Schemes for Hyperbolic Conservation Laws
The numerical simulation of compressible, turbulent flows requires an algorithm with high spectral resolution to capture all relevant length scales, as well as yield non-oscillatory solutions across discontinuities. Compact schemes (Lele, J. Comput. Phys., 1992) have significantly higher spectral resolutions than non-compact schemes of the same order of accuracy. A new class of weighted, non-linear compact schemes is presented in this talk that use solution-dependent WENO weights to yield high-resolution, non-oscillatory solutions. Fifth-order CR WENO schemes are derived and applied to scalar conservation laws and the inviscid Euler equations (Ghosh & Baeder, SIAM J. Sci. Comput., 2012).
The numerical properties are verified for benchmark problems and compared to those of the WENO schemes. Significant improvements are observed in the resolution of smaller length scales and discontinuities, as well as preservation of flow features over large convection distances. The schemes are integrated into a structured, finite-volume Navier-Stokes solver and applied to problems of practical relevance. Steady and unsteady flows around 2D airfoils and 3D wings/rotors are solved. Improvements are observed in the resolution of near-blade and wake flow features. The schemes are applied to overset meshes and it is verified that no additional modifications are necessary for the application of CRWENO schemes to such domains.
The direct numerical simulation (DNS) of canonical turbulent flows - the decay of isotropic turbulence and the sho ck-turbulence interaction - are attempted and the results presented. The CRWENO schemes show significant improvements in the resolution of smaller length scales. Overall, it is demonstrated that the CRWENO schemes are well-suited for problems with a large range of length scales