On the suppression of numerical oscillations using a non-linear filter

The idea of using a non-linear filtering algorithm to eliminate numerically generated oscillations is investigated. A detailed study is conducted to follow the development of numerical oscillations and their interaction with the filter. A relaxation procedure is also proposed to enhance the effectiveness of the filter. Three model problems, a 2D steady state scalar convection-diffusion equation, a ID unsteady gas dynamics flow with shock and a ID linear wave equation, have been designed to test the performance of the filtering algorithm. The effectiveness of the filter is assessed for convection schemes of different dispersive and diffusive characteristics, demonstrating that it is effective in eliminating oscillations with short wavelength, but oscillations of longer wavelengths are virtually unaffected. It is concluded that a proper combination of non-linear filter and dispersive numerical scheme is a viable alternative to dissipative schemes in resolving flows with sharp gradients and discontinuities