A low communication and large time step explicit finite-volume solver for non-hydrostatic atmospheric dynamics

Norman, Matthew R.; Nair, Ramachandran D.; Semazzi, Fredrick H. M.

doi:10.1016/j.jcp.2010.11.022

Cited by 35 publications

(35 citation statements)

References 40 publications

(26 reference statements)

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“…Explicit LTS schemes also have the advantage of being easily parallelizable, in contrast to implicit schemes, as pointed out by e.g. Norman et al [20]. One of the first large time step schemes for scalar conservation laws was presented by LeVeque [9] in 1982.…”

Section: Introductionmentioning

confidence: 99%

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A Large Time Step Roe Scheme Applied to Two-Phase Flow

Lindqvist¹,

Lund²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. We consider a large time step (LTS) Roe scheme, originally suggested by LeVeque [Comm. Pure Appl. Math., 37 (1984), pp. 463-477] which has attained increased popularity in recent years. The scheme is based on a wave formulation of the ordinary Roe scheme, and the assumption that waves interact linearly. This assumption lets us propagate waves over more than one cell, thereby violating the ordinary CFL condition requiring the Courant number to be less than one. The LTS Roe scheme is applied to a two-phase flow model with phase transfer, modelled using the stiffened-gas equation of state. Results from various test cases show that the LTS Roe scheme with moderate Courant numbers is significantly more efficient than the ordinary Roe scheme, measured by an error-to-runtime ratio. The optimal Courant number is mainly a trade-off between reduced runtime due to fewer time steps, and increased error due to the assumption of linear wave interactions.

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Section: Introductionmentioning

confidence: 99%

“…More recently, Qian and Lee [21] extended this scheme by taking wave interactions into account. Norman et al [20] developed a LTS scheme similar to LeVeque's approach, based on a WENO discretization.…”

Section: Introductionmentioning

confidence: 99%

A Large Time Step Roe Scheme Applied to Two-Phase Flow

Lindqvist¹,

Lund²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…This reduced accuracy at the longest time step is the reason why the simulations presented above did not use the longest stable time step. For the rising bubble test case, Norman et al (2011) also show the maximum u and vertical velocity for each time step as a function of resolution. Similar plots to theirs are shown in the bottom of Fig.…”

Section: ) Test Case Resultsmentioning

confidence: 99%

Curl-Free Pressure Gradients over Orography in a Solution of the Fully Compressible Euler Equations with Implicit Treatment of Acoustic and Gravity Waves

Weller

Shahrokhi

2014

Monthly Weather Review

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Steep orography can cause noisy solutions and instability in models of the atmosphere. A new technique for modeling flow over orography is introduced that guarantees curl-free gradients on arbitrary grids, implying that the pressure gradient term is not a spurious source of vorticity. This mimetic property leads to better hydrostatic balance and better energy conservation on test cases using terrain-following grids. Curl-free gradients are achieved by using the covariant components of velocity over orography rather than the usual horizontal and vertical components.In addition, gravity and acoustic waves are treated implicitly without the need for mean and perturbation variables or a hydrostatic reference profile. This enables a straightforward description of the implicit treatment of gravity waves.Results are presented of a resting atmosphere over orography and the curl-free pressure gradient formulation is advantageous. Results of gravity waves over orography are insensitive to the placement of terrain-following layers. The model with implicit gravity waves is stable in strongly stratified conditions, with NDt up to at least 10 (where N is the Brunt-Väisälä frequency). A warm bubble rising over orography is simulated and the curl-free pressure gradient formulation gives much more accurate results for this test case than a model without this mimetic property.

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“…Explicit Large Time Step (LTS) schemes are being increasingly used in the context of Computational Fluid Dynamics [1,2,3]. Apart from retaining most of the advantages offered by explicit schemes, they are able to increase not only the efficiency in terms of computational burden, but also the accuracy of the numerical results.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, the extension of the LTS scheme to the 2D shallow water equations was firstly mentioned in [10]. Other recent applications in connection with atmospheric dynamics [2] and Euler equations [1] have been extended to more than one dimension using the dimensional splitting technique. In this work, the extension of the mentioned LTS scheme to the 2D shallow water equations is achieved by means of this dimensional splitting procedure on structured grids.…”

Section: Introductionmentioning

confidence: 99%

A 2D extension of a Large Time Step explicit scheme (CFL>1) for unsteady problems with wet/dry boundaries

Morales-Hernändez

Hubbard

García‐Navarro

2014

Journal of Computational Physics

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A 2D Large TimeStep (LTS) explicit scheme on structured grids is presented in this work. It is first detailed and analysed for the 2D linear advection equation and then applied to the 2D shallow water equations. The dimensional splitting technique allows us to extend the ideas developed in the 1D case related to source terms, boundary conditions and the reduction of the time step in the presence of large discontinuities. The boundary conditions treatment as well as the wet/dry fronts in the case of the 2D shallow water equations require extra effort. The proposed scheme is tested on linear and non-linear equations and systems, with and without source terms. The numerical results are compared with those of the conventional scheme as well as with analytical solutions and experimental data.

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A low communication and large time step explicit finite-volume solver for non-hydrostatic atmospheric dynamics

Cited by 35 publications

References 40 publications

A Large Time Step Roe Scheme Applied to Two-Phase Flow

A Large Time Step Roe Scheme Applied to Two-Phase Flow

Curl-Free Pressure Gradients over Orography in a Solution of the Fully Compressible Euler Equations with Implicit Treatment of Acoustic and Gravity Waves

A 2D extension of a Large Time Step explicit scheme (CFL>1) for unsteady problems with wet/dry boundaries

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