A class of high-order dissipative compact schemes

Abstract

Central type compact schemes have no dissipative effects at the high wavenumbers. However, significant dispersive and parasite errors are associated with these wavenumbers. Throughout the course of numerical simulations, these high-wave-number waves propagate with erroneous directions and phase speeds, and will eventually destroy the solutions. In this paper we develope a class of high-order one-parameter dissipative schemes based on central compact schemes. The main feature of these schemes is that the grid stencils are the same as corresponding central compact schemes. By appropriately selecting the parameter, the dispersion of the schemes is improved and the dissipative effects are confined to high wavenumbers. This is helpfull to remove the high wavenumber errors and keep high resolution for the low and intermediate wavenumbers. We also discussed the boundary compact schemes, especially their dissipative feature. The numerical results for one dimensional convection equation show the effectiveness of these schemes to damp out the dispersive and parasite errors.