Hybrid Compact-WENO Finite Difference Scheme For Detonation Waves Simulations

The performance of a hybrid compact (Compact) finite difference scheme and characteristic-wise weighted essentially non-oscillatory (WENO) finite difference scheme (Hybrid) for the detonation waves simulations is investigated. The Hybrid scheme employs the nonlinear 5th-order WENO-Z scheme to capture high gradients and discontinuities in an essentially non-oscillatory manner and the linear 6th-order Compact scheme to resolve the fine scale structures in the smooth regions of the solution in an efficient and accurate manner. Numerical oscillations generated by the Compact scheme is mitigated by the high order filtering. The high order multi-resolution algorithm is employed to detect the smoothness of the solution. The Hybrid scheme allows a potential speedup up to a factor of three or more for certain classes of shocked problems. The simulations of one-dimensional shock-entropy wave interaction and classical stable detonation waves, and the two-dimensional detonation diffraction problem around a 90∘ corner show that the Hybrid scheme is more efficient, less dispersive and less dissipative than the WENO-Z scheme.