Dedalus: A flexible framework for numerical simulations with spectral methods

Burns, Keaton J.; Vasil, Geoffrey M.; Oishi, Jeffrey S.; Lecoanet, Daniel; Brown, Benjamin

doi:10.1103/physrevresearch.2.023068

Cited by 316 publications

(248 citation statements)

References 136 publications

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“…where 1 − θ M is the effective temperature difference across the fluid layer and h is the averaged fluid depth as defined in equation (10). Note that this definition of an effective Rayleigh number is analogous to the one described by [15] for the case of thermal convection interacting with a stably-stratified fluid layer above.…”

Section: B Convection Onsetmentioning

confidence: 98%

“…The problem described above is solved numerically by using a mixed pseudo-spectral fourth-order finite-difference method [22,24] and the particular phase-field model which has been discussed and validated in [23]. For several cases, we also checked our results by using the open-source pseudo-spectral solver Dedalus [9,10] (more information at http://dedalus-project.org).…”

Section: Mathematical Modelmentioning

confidence: 99%

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Bistability in Rayleigh-Bénard convection with a melting boundary

et al. 2020

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A pure and incompressible material is confined between two plates such that it is heated from below and cooled from above. When its melting temperature is comprised between these two imposed temperatures, an interface separating liquid and solid phases appears. Depending on the initial conditions, freezing or melting occurs until the interface eventually converges towards a stationary state. This evolution is studied numerically in a two-dimensional configuration using a phase-field method coupled with the Navier-Stokes equations. Varying the control parameters of the model, we exhibit two types of equilibria: diffusive and convective. In the latter case, Rayleigh-Bénard convection in the liquid phase shapes the solid-liquid front, and a macroscopic topography is observed. A simple way of predicting these equilibrium positions is discussed and then compared with the numerical simulations. In some parameter regimes, we show that multiple equilibria can coexist depending on the initial conditions. We also demonstrate that, in this bi-stable regime, transitioning from the diffusive to the convective equilibrium is inherently a nonlinear mechanism involving finite amplitude perturbations.

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Section: B Convection Onsetmentioning

confidence: 98%

Section: Mathematical Modelmentioning

confidence: 99%

Bistability in Rayleigh-Bénard convection with a melting boundary

et al. 2020

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“…where P u gives one condition at the left boundary (x = 0) and P s gives two conditions at the right boundary (x = L). The boundary value problem is solved using the Newton solver in the open-source Dedalus framework [7] until the update is smaller than the tolerance of…”

Section: Methodsmentioning

confidence: 99%

Predicting critical ignition in slow-fast excitable models

Marcotte

Biktashev

2020

Phys. Rev. E

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Linearization around unstable travelling waves in excitable systems can be used to approximate strength-extent curves in the problem of initiation of excitation waves for a family of spatially confined perturbations to the rest state. This theory relies on the knowledge of the unstable travelling wave solution as well as the leading left and right eigenfunctions of its linearization. We investigate the asymptotics of these ingredients, and utility of the resulting approximations of the strengthextent curves, in the slow-fast limit in two-component excitable systems of FitzHugh-Nagumo type, and test those on four illustrative models. Of these, two are with degenerate dependence of the fast kinetic on the slow variable, a feature which is motivated by a particular model found in the literature. In both cases, the unstable travelling wave solution converges to a stationary "critical nucleus" of the corresponding one-component fast subsystem. We observe that in the full system, the asymptotics of the left and right eigenspaces are distinct. In particular, the slow component of the left eigenfunction corresponding to the translational symmetry does not become negligible in the asymptotic limit. This has a significant detrimental effect on the critical curve predictions. The theory as formulated previously uses an heuristic to address a difficulty related to the translational invariance. We describe two alternatives to that heuristic, which do not use the misbehaving eigenfunction component. These new heuristics show much better predictive properties, including in the asymptotic limit, in all four examples.

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“…We outline the simulation set-up below, but for more details (including the scalings used for non-dimensionalization)are given in section 2 of Lecoanet and Jeevanjee (2019). Simulations are run with Dedalus, an open source pseudo-spectral framework (Burns et al 2019). We solve the non-dimensionalized Boussinesq equations:…”

Section: Simulation Set-upmentioning

confidence: 99%

Buoyancy‐driven entrainment in dry thermals

McKim

Jeevanjee

Lecoanet

2019

Quart J Royal Meteoro Soc

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Over 50 years ago it was proposed that dry thermals entrain because of buoyancy (via a constraint which requires an increase in the radius a). However, this runs counter to the scaling arguments commonly used to derive the entrainment rate, which rely on either the self‐similarity or a turbulent entrainment hypothesis. The assumption of turbulence‐driven entrainment has been investigated and it has been found that the entrainment efficiency e varies by less than 20% between laminar (Re=630) and turbulent (Re=6300) thermals. This motivated us to utilize the argument of buoyancy‐controlled entrainment in addition to the thermal's vertical momentum equation to build a model for thermal dynamics which does not invoke turbulence or self‐similarity. We derive simple expressions for the thermals' kinematic properties and their fractional entrainment rate ϵ and find close quantitative agreement with the values in direct numerical simulations. In particular, our expression for entrainment rate is consistent with the parametrization ϵ∼B/w2, for Archimedean buoyancy B and vertical velocity w. We also directly validate the role of buoyancy‐driven entrainment by running simulations where gravity is turned off midway through a thermal's rise. The entrainment efficiency e is observed to drop to less than one third of its original value in both the laminar and turbulent cases when g=0, affirming the central role of buoyancy in entrainment for dry thermals.

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Dedalus: A flexible framework for numerical simulations with spectral methods

Cited by 316 publications

References 136 publications

Bistability in Rayleigh-Bénard convection with a melting boundary

Bistability in Rayleigh-Bénard convection with a melting boundary

Predicting critical ignition in slow-fast excitable models

Buoyancy‐driven entrainment in dry thermals

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