Effect of explicit residual filtering on the stability of finite difference methods
Document Type
Article
Publication Date
4-4-2026
Abstract
Filtering is a core component of Large Eddy Simulations (LES) used to evaluate turbulent flows. Explicitly-defined filters can be utilized to tightly control the range of scales which propagate through the solution if properly applied. This work evaluates the effect of explicit, residual filtering on the Euler equations to investigate its effect on numerical stability in the absence of the dissipative viscous terms present in LES formations. Analysis is performed for 4th-order Runge-Kutta (RK), 1st order forward, and Lax-Friedrichs (LF) temporal finite differences using 2nd order central spatial schemes. The impact of filtering all equations or omitting the filter for the mass equation is compared for each method, identifying the destabilization effect of partial filtering, independent of the filter chosen. The RK temporal scheme also demonstrates improved stability limits as the filter ratio is increased. The LF method further provides a case of instability induced by filtering dependent on the residual definition.
Source Publication
Journal of Computational Physics (ISSN 0021-9991)
Recommended Citation
Theuerkauf, S. W., & Oefelein, J. C. (2026). Effect of explicit residual filtering on the stability of finite difference methods. Journal of Computational Physics, 559(15 August), 114876. https://doi.org/10.1016/j.jcp.2026.114876
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