Time-stepping approach for solving upper-bound problems: Application to two-dimensional Rayleigh-Benard convection

dc.contributor.utaustinauthorWen, Baoleen_US
dc.creatorWen, Baole L.en_US
dc.creatorChini, Gregory P.en_US
dc.creatorKerswell, Rich R.en_US
dc.creatorDoering, Charles R.en_US
dc.date.accessioned2017-07-18T20:11:14Z
dc.date.available2017-07-18T20:11:14Z
dc.date.issued2015-10en_US
dc.description.abstractAn alternative computational procedure for numerically solving a class of variational problems arising from rigorous upper-bound analysis of forced-dissipative infinite-dimensional nonlinear dynamical systems, including the Navier-Stokes and Oberbeck-Boussinesq equations, is analyzed and applied to Rayleigh-Benard convection. A proof that the only steady state to which this numerical algorithm can converge is the required global optimal of the relevant variational problem is given for three canonical flow configurations. In contrast with most other numerical schemes for computing the optimal bounds on transported quantities (e.g., heat or momentum) within the "background field" variational framework, which employ variants of Newton's method and hence require very accurate initial iterates, the new computational method is easy to implement and, crucially, does not require numerical continuation. The algorithm is used to determine the optimal background-method bound on the heat transport enhancement factor, i.e., the Nusselt number (Nu), as a function of the Rayleigh number (Ra), Prandtl number (Pr), and domain aspect ratio L in two-dimensional Rayleigh-Benard convection between stress-free isothermal boundaries (Rayleigh's original 1916 model of convection). The result of the computation is significant because analyses, laboratory experiments, and numerical simulations have suggested a range of exponents alpha and beta in the presumed Nu similar to (PrRa beta)-Ra-alpha scaling relation. The computations clearly show that for Ra <= 10(10) at fixed L = 2 root 2, Nu <= 0.106Pr(0)Ra(5/12), which indicates that molecular transport cannot generally be neglected in the "ultimate" high-Ra regime.en_US
dc.description.departmentInstitute for Computational Engineering and Sciences (ICES)en_US
dc.description.sponsorshipNSF DMS-0928098 DMS-1515161 DMS-0927587 PHY-1205219en_US
dc.description.sponsorshipSimons Foundationen_US
dc.description.sponsorshipNSFen_US
dc.description.sponsorshipONRen_US
dc.identifierdoi:10.15781/T2JW87346
dc.identifier.citationWen, Baole, Gregory P. Chini, Rich R. Kerswell, and Charles R. Doering. "Time-stepping approach for solving upper-bound problems: Application to two-dimensional Rayleigh-Bénard convection." Physical Review E 92, no. 4 (2015): 043012.en_US
dc.identifier.doi10.1103/PhysRevE.92.043012en_US
dc.identifier.issn1539-3755en_US
dc.identifier.urihttp://hdl.handle.net/2152/61166
dc.language.isoEnglishen_US
dc.relation.ispartofUT Faculty/Researcher Worksen_US
dc.relation.ispartofserialPhysical Review Een_US
dc.rightsAdministrative deposit of works to Texas ScholarWorks: This works author(s) is or was a University faculty member, student or staff member; this article is already available through open access or the publisher allows a PDF version of the article to be freely posted online. The library makes the deposit as a matter of fair use (for scholarly, educational, and research purposes), and to preserve the work and further secure public access to the works of the University.en_US
dc.rights.restrictionopenen_US
dc.subjectprandtl-number convectionen_US
dc.subjectheat-transporten_US
dc.subjectenergy-dissipationen_US
dc.subjectincompressible flowsen_US
dc.subjectvariational boundsen_US
dc.subjectboussinesq convectionen_US
dc.subjectturbulent convectionen_US
dc.subjectthermal-convectionen_US
dc.subjectporous layeren_US
dc.subjectshear-flowen_US
dc.titleTime-stepping approach for solving upper-bound problems: Application to two-dimensional Rayleigh-Benard convectionen_US
dc.typeArticleen_US

Access full-text files

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
Wen_2015.pdf
Size:
533.22 KB
Format:
Adobe Portable Document Format

License bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.65 KB
Format:
Plain Text
Description: