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A TEMPORAL APPROXIMATE DECONVOLUTION MODEL FOR LES

C. David Pruett
Department of Mathematics & Statistics, James Madison University Harrisonburg, VA 22807, USA

Benjamin C. Thomas
Department of Mathematics & Statistics, James Madison University Harrisonburg, Virginia 22807, USA

Chester E. Grosch
Center for Coastal Physical Oceanography and Ocean, Earth and Atmospheric Sciences, Old Dominion University, Norfolk, Virginia 23529, USA

Thomas B. Gatski


Résumé

The approximate deconvolution model of Stolz and Adams (1999) has proven itself a practical and effective method for residual-stress modeling in large-eddy simulation. Innovative in many regards, the model is conventional in the sense that it exploits spatial filtering to separate resolved and unresolved scales of motion. On the other hand, although largely unexplored territory, time-domain filtering for large-eddy simulation offers both conceptual and practical advantages under certain circumstances. A natural question therefore arises: Can the approximate deconvolution model be adapted for time-domain filtering, and if so, how? The current paper explores one such approach. The particular temporal approximate deconvolution model developed herein exploits explicit time-domain filtering by means of a causal exponential filter expressed in differential form. The unavoidable phase error of causal filtering necessitates adaptations to the baseline (spatial) model. Specifically, both the residual-stress and secondary regularization components of the model require careful design to avoid instability. Proper design, however, appears to lead to a family of robust temporal approximate deconvolution models. The current model is demonstrated by temporal large-eddy simulation of plane-channel flow at nominal Reτ = 180 and Reτ = 590. These results are encouraging and suggest that the temporal model can perform on a par with the spatial approximate deconvolution model, thereby providing a viable alternative whenever circumstances warrant.