TY - GEN

T1 - Physics-based stabilization of spectral elements for the 3D euler equations of moist atmospheric convection

AU - Marras, Simone

AU - Müller, Andreas

AU - Giraldo, Francis X.

N1 - Funding Information:
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.
Publisher Copyright:
© Springer International Publishing Switzerland 2015.

PY - 2015

Y1 - 2015

N2 - 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 highorder 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.

AB - 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 highorder 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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U2 - 10.1007/978-3-319-19800-2_32

DO - 10.1007/978-3-319-19800-2_32

M3 - Conference contribution

AN - SCOPUS:84951992014

SN - 9783319197999

T3 - Lecture Notes in Computational Science and Engineering

SP - 355

EP - 363

BT - Spectral and High Order Methods for Partial Differential Equations, ICOSAHOM 2014, Selected papers from the ICOSAHOM

A2 - Kirby, Robert M.

A2 - Berzins, Martin

A2 - Hesthaven, Jan S.

PB - Springer Verlag

T2 - 10th International Conference on Spectral and High-Order Methods, ICOSAHOM 2014

Y2 - 23 June 2014 through 27 June 2014

ER -