Efficient construction of unified continuous and discontinuous Galerkin formulations for the 3D Euler equations

Abdi, Daniel S.; Giraldo, Francis X.

doi:10.1016/j.jcp.2016.05.033

Cited by 23 publications

(23 citation statements)

References 38 publications

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“…A spherical perturbation of radius r 0 = 250 m, located at

((), x_{0}, y_{0}, z_{0}) = ((), 0, 0, 350) normalm

is added to the background state. The perturbation is defined by

θ^{'} = ({, \begin{matrix} array \\ array A [1 + \cos (\frac{π r}{r_{0}})] & array r \leq r_{0}, \\ array 0 & array r > r_{0}, \end{matrix})

with

r = \sqrt{([], {((), x - x_{0})}^{2} + {((), y - y_{0})}^{2} + {((), z - z_{0})}^{2})}

and A = 0.25 K as in Abdi and Giraldo (). Snapshots of the bubble at t = 0, 200 and 400 s are shown in Figure and a one‐dimensional cross‐section at x = y = 0 in Figure .…”

Section: Computational Examplesmentioning

confidence: 99%

See 1 more Smart Citation

A mixed finite‐element, finite‐volume, semi‐implicit discretization for atmospheric dynamics: Cartesian geometry

Melvin

Benacchio

Shipway

et al. 2019

Quart J Royal Meteoro Soc

101

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To meet the challenges posed by future generations of massively parallel supercomputers, a reformulation of the dynamical core for the Met Office's weather and climate model is presented. This new dynamical core uses explicit finite‐volume type discretizations for the transport of scalar fields coupled with an iterated‐implicit, mixed finite‐element discretization for all other terms. The target model aims to maintain the accuracy, stability and mimetic properties of the existing Met Office model independent of the chosen mesh while improving the conservation properties of the model. This paper details that proposed formulation and, as a first step towards complete testing, demonstrates its performance for a number of test cases in (the context of) a Cartesian domain. The new model is shown to produce similar results to both the existing semi‐implicit semi‐Lagrangian model used at the Met Office and other models in the literature on a range of bubble tests and orographically forced flows in two and three dimensions.

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“…A spherical perturbation of radius r 0 = 250 m, located at

((), x_{0}, y_{0}, z_{0}) = ((), 0, 0, 350) normalm

is added to the background state. The perturbation is defined by

θ^{'} = ({, \begin{matrix} array \\ array A [1 + \cos (\frac{π r}{r_{0}})] & array r \leq r_{0}, \\ array 0 & array r > r_{0}, \end{matrix})

with

r = \sqrt{([], {((), x - x_{0})}^{2} + {((), y - y_{0})}^{2} + {((), z - z_{0})}^{2})}

and A = 0.25 K as in Abdi and Giraldo (). Snapshots of the bubble at t = 0, 200 and 400 s are shown in Figure and a one‐dimensional cross‐section at x = y = 0 in Figure .…”

Section: Computational Examplesmentioning

confidence: 99%

“…and A = 0.25 K as in Abdi and Giraldo (2016). Snapshots of the bubble at t = 0, 200 and 400 s are shown in Figure 8 and a one-dimensional cross-section at x = y = 0 in Figure 9.…”

Section: D Rising Bubblementioning

confidence: 99%

A mixed finite‐element, finite‐volume, semi‐implicit discretization for atmospheric dynamics: Cartesian geometry

Melvin

Benacchio

Shipway

et al. 2019

Quart J Royal Meteoro Soc

101

View full text Add to dashboard Cite

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“…In many CFD applications, the finite-volume method is applied on a unstaggered grid using an approximate Riemann solver to calculate the volume interface fluxes. Therefore, despite performance difficulties, in recent years, many efforts have been made to implement the unstaggered Riemann solver for atmospheric applications (Abdi & Giraldo, 2016;Giraldo & Restelli, 2008;Katta et al, 2014;Kelly & Giraldo, 2012;Kopera & Giraldo, 2014;Ullrich et al, 2010;Ullrich & Jablonowski, 2012;Yang et al, 2010). However, compared to geophysical dynamical cores, the mathematical formulation of these solvers are complicated and computationally expensive.…”

Section: Introductionmentioning

confidence: 99%

Towards an Unstaggered Finite‐Volume Dynamical Core With a Fast Riemann Solver: 1‐D Linearized Analysis of Dissipation, Dispersion, and Noise Control

Chen

Lin

Harris

2018

J Adv Model Earth Syst

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Many computational fluid dynamics codes use Riemann solvers on an unstaggered grid for finite volume methods, but this approach is computationally expensive compared to existing atmospheric dynamical cores equipped with hyper‐diffusion or other similar relatively simple diffusion forms. We present a simplified Low Mach number Approximate Riemann Solver (LMARS), made computationally efficient through assumptions appropriate for atmospheric flows: low Mach number, weak discontinuities, and locally uniform sound speed. This work will examine the dissipative and dispersive properties of LMARS using Von Neumann linearized analysis to the one‐dimensional linearized shallow water equations. We extend these analyses to higher‐order methods by numerically solving the Fourier‐transformed equations. It is found that the pros and cons due to grid staggering choices diminish with high‐order schemes. The linearized analysis is limited to modal, smooth solutions using simple numerical schemes, and cannot analyze solutions with discontinuities. To address this problem, this work presents a new idealized test of a discontinuous wave packet, a single Fourier mode modulated by a discontinuous square wave. The experiments include studies of well‐resolved and (near) grid‐scale wave profiles, as well as the representation of discontinuous features and the results are validated against the Von Neumann analysis. We find the higher‐order LMARS produces much less numerical noise than do inviscid unstaggered and especially staggered schemes while retaining accuracy for better‐resolved modes.

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“…This new version of NUMA is capable of handling two data layouts for CG and one for DG -similar to the unified construction of numa2dCGDG_AMR, the 2D adaptive mesh refinement version of NUMA. This unification in the 3D code unifies all NUMA codes into a single code-base which will greatly simplify the further improvement of the model (for more details about the unified NUMA code see Abdi and Giraldo [3]).…”

Section: Approachmentioning

confidence: 99%

“…After year 2, the first stage of unification of the CG and DG codes was completed [3]. This resulted in a single code base that can solve the Euler equations using either CG or DG.…”

Section: Figure 1: Overview Of Occa Api Kernel Languages and Programentioning

confidence: 99%

NPS-NRL-Rice-UIUC Collaboration on Navy Atmosphere-Ocean Coupled Models on Many-Core Computer Architectures Annual Report

Wilcox

Giraldo²,

Campbell³

et al. 2015

Self Cite

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DynamicsExplicit-in-time CG a continuous Galerkin discretization of the compressible Euler mini-app with explicit time integration;Explicit-in-time DG a discontinuous Galerkin discretization of the compressible Euler mini-app with explicit time integration;Vertically Semi-Implicit CG a continuous Galerkin discretization of the compressible Euler mini-app with vertically implicit semi-implicit time integration;Vertically Semi-Implicit DG a discontinuous Galerkin discretization of the compressible Euler mini-app with vertically implicit semi-implicit time integration;Once the performance of a mini-app is accepted it will be considered for adoption into NUMA. Extending the kernels in NUMA is being lead by Giraldo and his postdoctoral researcher Abdi. We will also make these mini-apps available to the community to be imported into other codes if desired. Wilcox is working closely with Warburton and his team to lead the effort to develop the mini-apps including hand rolled computational kernels optimized for GPU accelerators. These kernels are "hand-written" in OCCA, a library Warburton's group is developing that allows a single kernel to be compiled using many different threading frameworks, such as CUDA, OpenCL, OpenMP, and Pthreads. We are initially developing hand-written kernels to provide a performance target for the Loo.py generated kernels. Parallel communication between computational nodes will use the MPI standard to enable the mini-apps to run on large scale clusters. Using these community standards for parallel programing will allow our mini-apps to be portable to many platforms, however the performance may not be portable across devices. For performance portability, we, lead by Klöckner, are using Loo.py to generate OCCA kernels which can be automatically tuned for current many-core devices along with future ones.The second objective is to expand (as needed by the mini-apps) the OCCA and Loo.py efforts, lead by Warburton and Klöckner. These will be extended naturally in tandem with the requirements that emerge during the development of the mini-apps. We will take a pragmatic approach where features will only be added as they are needed by the mini-apps or will aid in the transition of the mini-app technology back into NUMA. For the sharing part of the objective, both OCCA and Loo.py are open source and can be downloaded from https://github.com/libocca/occa and https://github.com/inducer/loopy, respectively. They are operational and are ready to be evaluated for use in other projects. As it warrants, we will give presentations and demonstrations of the tools to help increase their adoption.The third objective, lead by Campbell, is to implement NEPTUNE as an ESMF component. This will be done in collaboration with the developers of NEPTUNE at NRL Monterey. Once NEPTUNE has been made a component, we will move to running the coupled air-ocean-wave-ice system involving NEPTUNE (with NUMA as its dynamical core), HYCOM, Wavewatch III, and CICE within the Navy ESPC. WORK COMPLETEDIn the course of this project we p...

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Efficient construction of unified continuous and discontinuous Galerkin formulations for the 3D Euler equations

Cited by 23 publications

References 38 publications

A mixed finite‐element, finite‐volume, semi‐implicit discretization for atmospheric dynamics: Cartesian geometry

A mixed finite‐element, finite‐volume, semi‐implicit discretization for atmospheric dynamics: Cartesian geometry

Towards an Unstaggered Finite‐Volume Dynamical Core With a Fast Riemann Solver: 1‐D Linearized Analysis of Dissipation, Dispersion, and Noise Control

NPS-NRL-Rice-UIUC Collaboration on Navy Atmosphere-Ocean Coupled Models on Many-Core Computer Architectures Annual Report

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