Continuation of probability density functions using a generalized Lyapunov approach

Journal Article · Mon May 01 00:00:00 EDT 2017 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2017.02.021· OSTI ID:22622292

Baars, S., E-mail: [e-mail] ^[1]; Viebahn, J.P., E-mail: [e-mail] ^[2]; Mulder, T.E., E-mail: [e-mail] ^[3]; Kuehn, C., E-mail: [e-mail] ^[4]; Wubs, F.W., E-mail: [e-mail] ^[1]; Dijkstra, H.A., E-mail: [e-mail] ^[3]; School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY ^[5]

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1. Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK Groningen (Netherlands)
2. Centrum Wiskunde & Informatica (CWI), P.O. Box 94079, 1090 GB, Amsterdam (Netherlands)
3. Institute for Marine and Atmospheric research Utrecht, Department of Physics and Astronomy, Utrecht University, Princetonplein 5, 3584 CC Utrecht (Netherlands)
4. Technical University of Munich, Faculty of Mathematics, Boltzmannstr. 3, 85748 Garching bei München (Germany)
5. (United States)

Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining probability density functions of systems of stochastic partial differential equations near fixed points, under a small noise approximation. Key innovation is the efficient solution of a generalized Lyapunov equation using an iterative method involving low-rank approximations. We apply and illustrate the capabilities of the method using a problem in physical oceanography, i.e. the occurrence of multiple steady states of the Atlantic Ocean circulation.

• OSTI ID: 22622292
• Journal Information: Journal of Computational Physics, Vol. 336; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
BIFURCATION
FLUID FLOW
FLUIDS
INSTABILITY
ITERATIVE METHODS
LYAPUNOV METHOD
MATHEMATICAL SOLUTIONS
NOISE
OCEANOGRAPHY
PARTIAL DIFFERENTIAL EQUATIONS
PROBABILITY
PROBABILITY DENSITY FUNCTIONS
STEADY-STATE CONDITIONS
STOCHASTIC PROCESSES