On the filtering of spurious oscillations in the numerical simulations of convection dominated problems

Vietnam Journal of Mathematics, 47 (2019), 851–864
https://link.springer.com/article/10.1007/s10013-019-00369-z

This paper presents the numerical filtering as a valuable tool used for the removal of spurious oscillations in the numerical solution of some specific fluids flows. The qualitative results based on the application of two distinct representative filters are discussed. The compact low-pass filters and the digital Total Variation Diminishing (TVD) filters are described as examples of the filtering approach. Their use is shown on selected one-dimensional advection problems, demonstrating the essential behavior of the filtered solution. Finally an example of a more realistic biomedical problem solved using finite-volume scheme is discussed including the effect of the digital filter. The conclusions sum up some of the experience from the application of both filtering techniques.