High resolution conjugate filters for hyperbolic conservation laws

A new realization of the conjugate filter oscillation (CFOR) scheme based on the Hermite kernel is proposed for hyperbolic conservation laws. Such a realization is found to give a nearly optimal resolution and a better approximation to the low-pass filter than the previous kernels. Typical one- and two-dimensional numerical examples, with or without shocks, axe employed to explore the utility, test the resolution and examine the stability of the present CFOR-Hermite scheme. Small ratio of point-per-wavelength (PPW) is achieved in advancing a wavepacket and in resolving the interaction of shock/entropy wave. The present results for the advection of an isotropic vortex compare very favorably to those in the literature.