Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES

Marras, Simone; Nazarov, Murtazo; Giraldo, Francis X.

doi:10.1016/j.jcp.2015.07.034

Cited by 31 publications

(37 citation statements)

References 45 publications

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“…Tompkins and Semie () have illustrated the importance of the sub‐grid turbulence scheme at cloud permitting resolutions, exerting strong control over moisture entrainment, the thermodynamic properties of convecting cores and large‐scale organization. While a numerical filter should not be confused as a turbulence closure (Jablonowski & Williamson, ), unless, perhaps if it is explicitly designed for that purpose (e.g., Grinstein et al, ; Marras et al, ), there is certainly the possibility that modulating the strength of the numerical filter might act as some form of entrainment parameter for the grid‐scale thermals in AGCM simulations. On the other hand, it has been argued that AGCMs are overly dissipative (Berner et al, ; Shutts, ), implying that additional damping resulting from a longer physics time step is not preferred.…”

Section: Discussionmentioning

confidence: 99%

An Idealized Test of the Response of the Community Atmosphere Model to Near‐Grid‐Scale Forcing Across Hydrostatic Resolutions

Herrington

Reed

2018

J Adv Model Earth Syst

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A set of idealized experiments are developed using the Community Atmosphere Model (CAM) to understand the vertical velocity response to reductions in forcing scale that is known to occur when the horizontal resolution of the model is increased. The test consists of a set of rising bubble experiments, in which the horizontal radius of the bubble and the model grid spacing are simultaneously reduced. The test is performed with moisture, through incorporating moist physics routines of varying complexity, although convection schemes are not considered. Results confirm that the vertical velocity in CAM is to first‐order, proportional to the inverse of the horizontal forcing scale, which is consistent with a scale analysis of the dry equations of motion. In contrast, experiments in which the coupling time step between the moist physics routines and the dynamical core (i.e., the “physics” time step) are relaxed back to more conventional values results in severely damped vertical motion at high resolution, degrading the scaling. A set of aqua‐planet simulations using different physics time steps are found to be consistent with the results of the idealized experiments.

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Section: Discussionmentioning

confidence: 99%

An Idealized Test of the Response of the Community Atmosphere Model to Near‐Grid‐Scale Forcing Across Hydrostatic Resolutions

Herrington

Reed

2018

J Adv Model Earth Syst

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“…The initial flow is static and in hydrostatic balance. An isothermal equilibrium is considered with a sinusoidal gravitational field potential [41,54] ϕ − 1 2π sin2πy (58) specified on a periodic domain 0 ≤ y < 1. The gravitational force in Eq.…”

Section: A Well-balanced Testsmentioning

confidence: 99%

“…This difference is due to the treatment of subgrid-length scales. The NUMA solver stabilizes the solution through a residual-based dynamic subgridscale model [57,58] designed for large-eddy simulation, whereas the WENO5 solution to the inviscid Euler equations relies on the linear and nonlinear numerical diffusion to stabilize the unresolved scales. Incorporation of a subgrid-scale model in the current solver will be explored in the future.…”

Section: Rising Thermal Bubblementioning

confidence: 99%

Well-Balanced, Conservative Finite Difference Algorithm for Atmospheric Flows

Ghosh

Constantinescu

2016

AIAA Journal

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“…[5,6,7,8,9,10] for a non-exhaustive overview. Nowadays, the main challenge is to develop efficient high order numerical methods which are able to capture even small scale structures of the flow, avoiding the use of RANS turbulence models (see [11,12]). In this paper, we propose a novel family of high order accurate staggered semi-implicit discontinuous Galerkin (DG) methods, which extends the works presented in [1,3,4] appropriately to deal also with gravity driven flows.…”

Section: Introductionmentioning

confidence: 99%

Efficient high order accurate staggered semi-implicit discontinuous Galerkin methods for natural convection problems

et al. 2020

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In this article we propose a new family of high order staggered semi-implicit discontinuous Galerkin (DG) methods for the simulation of natural convection problems. Assuming small temperature fluctuations, the Boussinesq approximation is valid and in this case the flow can simply be modeled by the incompressible Navier-Stokes equations coupled with a transport equation for the temperature and a buoyancy source term in the momentum equation. Our numerical scheme is developed starting from the work presented in [1,2,3], in which the spatial domain is discretized using a face-based staggered unstructured mesh. The pressure and temperature variables are defined on the primal simplex elements, while the velocity is assigned to the dual grid. For the computation of the advection and diffusion terms, two different algorithms are presented: i) a purely Eulerian explicit upwind-type scheme and ii) a semi-Lagrangian approach. The first methodology leads to a conservative scheme whose major drawback is the time step restriction imposed by the CFL stability condition due to the explicit discretization of the convective terms. On the contrary, computational efficiency can be notably improved relying on a semi-Lagrangian approach in which the Lagrangian trajectories of the flow are tracked back. This method leads to an unconditionally stable scheme if the diffusive terms are discretized implicitly. Once the advection and diffusion contributions have been computed, the pressure Poisson equation is solved and the velocity is updated. As a second model for the computation of buoyancy-driven flows, in this paper we also consider the full compressible Navier-Stokes equations. The staggered semi-implicit DG method first proposed in [4] for all Mach number flows is properly extended to account for the gravity source terms arising in the momentum and energy conservation laws. In order to assess the validity and the robustness of our novel class of staggered semi-implicit DG schemes, several classical benchmark problems are considered, showing in all cases a good agreement with available numerical reference data. Furthermore, a detailed comparison between the incompressible and the compressible solver is presented. Finally, advantages and disadvantages of the Eulerian and the semi-Lagrangian methods for the discretization of the nonlinear convective terms are carefully studied.

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Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES

Cited by 31 publications

References 45 publications

An Idealized Test of the Response of the Community Atmosphere Model to Near‐Grid‐Scale Forcing Across Hydrostatic Resolutions

An Idealized Test of the Response of the Community Atmosphere Model to Near‐Grid‐Scale Forcing Across Hydrostatic Resolutions

Well-Balanced, Conservative Finite Difference Algorithm for Atmospheric Flows

Efficient high order accurate staggered semi-implicit discontinuous Galerkin methods for natural convection problems

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