Coral: a parallel spectral solver for fluid dynamics and partial differential equations

Abstract

Coral is a fast, flexible, and efficient time-stepper for solving a large class of partial differential equations, at the core of which are the Navier-Stokes equations that govern fluid motions. Written in Fortran and employing the MPI standard for parallelization, the scalability of Coral allows the code to leverage the resources of high-performance computing infrastructures (up to hundreds of thousands of core, see Li & Laizet ( 2010)), while running efficiently on laptops and workstations. Equations are entered by the user in the form of a plain text file following a simple and legible syntax. No coding proficiency in Fortran is required. This flexibility makes Coral suitable for both students and researchers with no coding experience.

Experimental observation of the geostrophic turbulence regime of rapidly rotating convection

“…Direct numerical simulations. We solve equations [5][6][7] inside a horizontally periodic domain with the pseudo-spectral solver Coral (52), previously used for non-rotating convective flows (31) and validated against both analytical results (53) and solutions computed with the Dedalus software (54). The bottom boundary is insulating and no-slip, while the top boundary is insulating and stress-free.…”

Velocity-informed upper bounds on the convective heat transport induced by internal heat sources and sinks

“…The measurement accuracy is insufficient to characterize the scaling behaviour of the dissipation coefficient more precisely, and we turn to numerical data instead. We compute numerical solutions to the governing equations (2.3) using Coral, a pseudo-spectral, scalable, time-stepping solver for differential equations [36]. The computational domain is a unit cube (x, y, z) ∈ [0, 1) × [0, 1) × [0, 1] with periodic boundary conditions along the horizontal directions (x, y).…”

“…We compute numerical solutions to the governing equations (2.3) using Coral, a pseudo-spectral, scalable, time-stepping solver for differential equations [36]. The computational domain is a unit cube false(x,y,zfalse)∈false[0,1false)×false[0,1false)×false[0,1false] with periodic boundary conditions along the horizontal directions false(x,yfalse).…”

“…The experimental and numerical data are available online (). The numerical code is publicly available, as described in [36].…”

Transport and emergent stratification in the equilibrated Eady model: the vortex-gas scaling regime

“…This leads to the two-layer QG (2LQG) model, where the governing equations reduce to a conservation equation for the potential vorticity (PV) inside each fluid layer (Phillips 1954). Even for this canonical model, however, the transport properties of the equilibrated turbulent flow in the moderate-to-low drag regime have been captured only recently by a scaling theory, which we coined the 'vortex-gas' scaling regime and extended to the β-plane (Gallet & Ferrari 2020, 2021.…”