Designing Effective Filters for Numerical Approximations to Hyperbolic Conservation Laws

Filtering for Hyperbolic Conservation Laws is increasingly important as mathematical and computational models improve and data becomes more accessible.
Filtering is an important tool to aid in reducing noise, errors, and the amount of data necessary in numerical models.
In this talk, the important properties necessary for designing effective filters will be discussed, how designing effective filters utilises information from the dual equation, and how the filter design is connected to the ability to extract the appropriate information in Fourier space.
The Smoothness-Increasing Accuracy-Conserving (SIAC) filter will be utilised to illustrate the main ideas.
 Lastly, the effectiveness in applications will be discussed.