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Fourier continuation method for incompressible fluids with boundaries

Fontana, Mauro and Bruno, Oscar P. and Mininni, Pablo D. and Dmitruk, Pablo (2020) Fourier continuation method for incompressible fluids with boundaries. Computer Physics Communications, 256 . Art. No. 107482. ISSN 0010-4655. doi:10.1016/j.cpc.2020.107482.

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We present a Fourier Continuation-based parallel pseudospectral method for incompressible fluids in cuboid non-periodic domains. The method produces dispersionless and dissipationless derivatives with fast spectral convergence inside the domain, and with very high order convergence at the boundaries. Incompressibility is imposed by solving a Poisson equation for the pressure. Being Fourier-based, the method allows for fast computation of spectral transforms. It is compatible with uniform grids (although refined or nested meshes can also be implemented), which in turn allows for explicit time integration at sufficiently high Reynolds numbers. Using a new parallel code named SPECTER we illustrate the method with two problems: channel flow, and plane Rayleigh-Bénard convection under the Boussinesq approximation. In both cases the method yields results compatible with previous studies using other high-order numerical methods, with mild requirements on the time step for stability.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Fontana, Mauro0000-0001-7636-9275
Bruno, Oscar P.0000-0001-8369-3014
Mininni, Pablo D.0000-0001-6858-6755
Additional Information:© 2020 Elsevier B.V. Received 10 March 2020, Revised 17 June 2020, Accepted 29 June 2020, Available online 2 July 2020. The review of this paper was arranged by David W. Walker. The authors acknowledge support from PIP Grant No. 11220150100324CO and from PICT Grant No. 2015-3530. This work was also supported by NSF and AFOSR through contracts DMS-1714169 and FA9550-15-1-0043, and by the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808. We also thank the Physics Department at the University of Buenos Aires for providing computing time on its Dirac cluster.
Funding AgencyGrant Number
Proyectos de Investigación Científica y Tecnológica (PICT)2015-3530
Air Force Office of Scientific Research (AFOSR)FA9550-15-1-0043
Vannevar Bush FellowshipUNSPECIFIED
National Security Science and Engineering Faculty FellowshipN00014-16-1-2808
Subject Keywords:Navier–Stokes equation; Non-periodic boundary conditions; Spectral methods; Fourier continuation; Explicit time-stepping; Simulations
Record Number:CaltechAUTHORS:20200702-121835661
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Official Citation:Mauro Fontana, Oscar P. Bruno, Pablo D. Mininni, Pablo Dmitruk, Fourier continuation method for incompressible fluids with boundaries, Computer Physics Communications, Volume 256, 2020, 107482, ISSN 0010-4655, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104207
Deposited By: Tony Diaz
Deposited On:02 Jul 2020 19:57
Last Modified:16 Nov 2021 18:29

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