On the Systematic Construction of Discrete Filters
Conference Paper,29 Apr 2019,30 May 2019
AIR FORCE RESEARCH LAB EDWARDS AFB CA EDWARDS AFB United States
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The design of numerical attenuation can in general be used to enhance solution stability and accuracy. For example, filtering plays a central role in controlling the impact of numerical errors in areas such as Large-Eddy Simulations. The following presentation considers the construction of finite difference type filters, focusing on how to incorporate important properties such as scale-separation, high-order, monotonicity, etc. These are studied with respect to the set of classic discrete Purser filters along with recent generalizations. Next, the use of such interior stencils on bounded domains is presented, focusing on preserving the energy-stability and conservational properties of the underlying solution. After further highlighting the link between filtering and artificial dissipation, the current approaches can be seen to form a systematic means of designing numerical dissipation schemes for appropriate use with time-accurate simulations.
- Numerical Mathematics