A stochastic particle-mesh scheme for uncertainty propagation in vortical flows

A new mesh-particle scheme is constructed for uncertainty propagation in vortical flow. The scheme is based on the incorporation of polynomial chaos (PC) expansions into a Lagrangian particle approximation of the Navier–Stokes equations. The main idea of the method is to use a unique set of particle...

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Bibliographic Details
Published in:Journal of computational physics 2007-09, Vol.226 (1), p.645-671
Main Authors: Le Maıˆtre, Olivier P., Knio, Omar M.
Format: Article
Language:English
Subjects:
ALGORITHMS
APPROXIMATIONS
CHAOS THEORY
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Computational techniques
Exact sciences and technology
FLUID FLOW
LAGRANGIAN FUNCTION
Mathematical methods in physics
MATHEMATICAL SOLUTIONS
NATURAL CONVECTION
NAVIER-STOKES EQUATIONS
Particle method
Physics
POLYNOMIALS
Spectral method
Stochastic polynomials
STOCHASTIC PROCESSES
Uncertainty
VALIDATION
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Summary:A new mesh-particle scheme is constructed for uncertainty propagation in vortical flow. The scheme is based on the incorporation of polynomial chaos (PC) expansions into a Lagrangian particle approximation of the Navier–Stokes equations. The main idea of the method is to use a unique set of particles to transport the stochastic modes of the solution. The particles are transported by the mean velocity field, while their stochastic strengths are updated to account for diffusive and convective effects induced by the coupling between stochastic modes. An integral treatment is used for the evaluation of the coupled stochastic terms, following the framework of the particle strength exchange (PSE) methods, which yields a conservative algorithm. It is also shown that it is possible to apply solution algorithms used in deterministic setting, including particle-mesh techniques and particle remeshing. Thus, the method combines the advantages of particles discretizations with the efficiency of PC representations. Validation of the method on uncertain diffusion and convection problems is first performed. An example is then presented of natural convection of a hot patch of fluid in infinite domain, and the computations are used to illustrate the effectiveness of the approach for both large number of particles and high-order PC expansions.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2007.04.030