Barmparousis, Christos and Drikakis, Dimitris 2017. Multidimensional quantification of uncertainty and application to a turbulent mixing model. International Journal for Numerical Methods in Fluids, Vol. 85, Issue. 7, p. 385.
Parussini, L. Venturi, D. Perdikaris, P. and Karniadakis, G.E. 2017. Multi-fidelity Gaussian process regression for prediction of random fields. Journal of Computational Physics, Vol. 336, p. 36.
Yigit, Sahin and Chakraborty, Nilanjan 2017. Rayleigh–Bénard Power-Law Fluid Convection in Rectangular Enclosures. Journal of Thermophysics and Heat Transfer, Vol. 31, Issue. 4, p. 805.
Karani, Hamid and Huber, Christian 2017. Transitional behaviour of convective patterns in free convection in porous media. Journal of Fluid Mechanics, Vol. 818,
Wang, Deli Xu, Wei and Zhao, Xiangrong 2016. Stationary responses of a Rayleigh viscoelastic system with zero barrier impacts under external random excitation. Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 26, Issue. 3, p. 033103.
Földes, J Glatt-Holtz, N E Richards, G and Whitehead, J P 2016. Ergodicity in randomly forced Rayleigh–Bénard convection. Nonlinearity, Vol. 29, Issue. 11, p. 3309.
Yigit, Sahin McRoberts, Calum and Chakraborty, Nilanjan 2016. Numerical investigation of laminar Rayleigh–Bénard convection of power-law fluids in square cross-sectional cylindrical annular enclosures. International Communications in Heat and Mass Transfer, Vol. 78, p. 112.
Li, You-Rong Hu, Yu-Peng Ouyang, Yu-Qing and Wu, Chun-Mei 2015. Flow state multiplicity in Rayleigh–Bénard convection of cold water with density maximum in a cylinder of aspect ratio 2. International Journal of Heat and Mass Transfer, Vol. 86, p. 244.
Cho, H. Yang, X. Venturi, D. and Karniadakis, G. E. 2015. Algorithms for Propagating Uncertainty Across Heterogeneous Domains. SIAM Journal on Scientific Computing, Vol. 37, Issue. 6, p. A3030.
Yigit, Sahin Poole, Robert J. and Chakraborty, Nilanjan 2015. Effects of aspect ratio on laminar Rayleigh–Bénard convection of power-law fluids in rectangular enclosures: A numerical investigation. International Journal of Heat and Mass Transfer, Vol. 91, p. 1292.
Hu, Yu-Peng Li, You-Rong and Wu, Chun-Mei 2015. Rayleigh-Bénard convection of cold water near its density maximum in a cubical cavity. Physics of Fluids, Vol. 27, Issue. 3, p. 034102.
Torres, Juan F. Henry, Daniel Komiya, Atsuki and Maruyama, Shigenao 2015. Transition from multiplicity to singularity of steady natural convection in a tilted cubical enclosure. Physical Review E, Vol. 92, Issue. 2,
Anandalakshmi, R. and Basak, Tanmay 2015. Natural convection in rhombic enclosures with isothermally heated side or bottom wall: Entropy generation analysis. European Journal of Mechanics - B/Fluids, Vol. 54, p. 27.
Benouared, Ouahiba Mamou, Mahmoud and Messaoudene, Noureddine Ait 2014. Numerical nonlinear analysis of subcritical Rayleigh-Bénard convection in a horizontal confined enclosure filled with non-Newtonian fluids. Physics of Fluids, Vol. 26, Issue. 7, p. 073101.
Choi, Minseok Sapsis, Themistoklis P. and Karniadakis, George Em 2014. On the equivalence of dynamically orthogonal and bi-orthogonal methods: Theory and numerical simulations. Journal of Computational Physics, Vol. 270, p. 1.
Cho, H. Venturi, D. and Karniadakis, G. E. 2013. Adaptive Discontinuous Galerkin Method for Response-Excitation PDF Equations. SIAM Journal on Scientific Computing, Vol. 35, Issue. 4, p. B890.
Sapsis, T. P. Ueckermann, M. P. and Lermusiaux, P. F. J. 2013. Global analysis of Navier–Stokes and Boussinesq stochastic flows using dynamical orthogonality. Journal of Fluid Mechanics, Vol. 734, p. 83.
Anandalakshmi, R. and Basak, Tanmay 2013. Heatline based thermal management for natural convection in porous rhombic enclosures with isothermal hot side or bottom wall. Energy Conversion and Management, Vol. 67, p. 287.
Stochastic bifurcations and stability of natural convection within two-dimensional square enclosures are investigated by different stochastic modelling approaches. Deterministic stability analysis is carried out first to obtain steady-state solutions and primary bifurcations. It is found that multiple stable steady states coexist, in agreement with recent results, within specific ranges of Rayleigh number. Stochastic simulations are then conducted around bifurcation points and transitional regimes. The influence of random initial flow states on the development of supercritical convection patterns is also investigated. It is found that a multi-element polynomial chaos method captures accurately the onset of convective instability as well as multiple convection patterns corresponding to random initial flow states.
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