Abstract
In the context of stabilization of high order spectral elements, we introduce a dissipative scheme based on the solution of the compressible Euler equations that are regularized through the addition of a residual-based stress tensor. Because this stress tensor is proportional to the residual of the unperturbed equations, its effect is close to none where the solution is sufficiently smooth, whereas it increases elsewhere. This paper represents a first extension of the work by Nazarov and Hoffman (Int J Numer Methods Fluids 71:339–357, 2013) to high-order spectral elements in the context of low Mach number atmospheric dynamics. The simulations show that the method is reliable and robust for problems with important stratification and thermal processes such as the case of moist convection. The results are partially compared against a Smagorinsky solution. With this work we mean to make a step forward in the implementation of a stabilized, high order, spectral element large eddy simulation (LES) model within the Nonhydrostatic Unified Model of the Atmosphere, NUMA.
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Notes
- 1.
The high-order spectral elements used for this study are built using Legendre-Gauss-Lobatto (LGL) integration and interpolation points.
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Acknowledgements
The authors are thankful to Dr. Murtazo Nazarov for his clarifications about the original method. They also gratefully acknowledge the support of the Office of Naval Research through program element PE-0602435N, the National Science Foundation (Division of Mathematical Sciences) through program element 121670, and the Air Force Office of Scientific Research through the Computational Mathematics program. The first and second authors were supported by the National Academies through a National Research Council fellowship.
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Marras, S., Müller, A., Giraldo, F.X. (2015). Physics-Based Stabilization of Spectral Elements for the 3D Euler Equations of Moist Atmospheric Convection. In: Kirby, R., Berzins, M., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Lecture Notes in Computational Science and Engineering, vol 106. Springer, Cham. https://doi.org/10.1007/978-3-319-19800-2_32
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