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Parallel high-order methods for dete...

Lin, Guang.

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Parallel high-order methods for deterministic and stochastic CFD and MHD problems.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Parallel high-order methods for deterministic and stochastic CFD and MHD problems./
Author:	Lin, Guang.
Description:	192 p.
Notes:	Adviser: George Em Karniadakis.
Contained By:	Dissertation Abstracts International68-07B.
Subject:	Applied Mechanics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3272010
ISBN:	9780549119791

Parallel high-order methods for deterministic and stochastic CFD and MHD problems.
Lin, Guang.

Parallel high-order methods for deterministic and stochastic CFD and MHD problems. - 192 p.

Adviser: George Em Karniadakis.

Thesis (Ph.D.)--Brown University, 2007.

In computational fluid dynamics (CFD) and magneto-hydro-dynamics (MHD) applications there exist many sources of uncertainty, arising from imprecise material properties, random geometric roughness, noise in boundary/initial condition, transport coefficients, or external forcing. In this dissertation, stochastic perturbation analysis and stochastic simulations based on multi-element generalized polynomial chaos (ME-gPC) are employed synergistically, to solve large-scale stochastic CFD and MHD problems with many random inputs. Stochastic analytical solutions are obtained to serve in verifying the accuracy of the numerical results for small random inputs, but also in shedding light into the physical mechanisms and scaling laws associated with the structural changes of flow field due to random inputs.

ISBN: 9780549119791Subjects--Topical Terms:

1018410
Applied Mechanics.

Parallel high-order methods for deterministic and stochastic CFD and MHD problems.
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020 $a 9780549119791
035 $a (UMI)AAI3272010
035 $a AAI3272010
040 $a UMI $c UMI
100 1 $a Lin, Guang. $3 1269488
245 1 0 $a Parallel high-order methods for deterministic and stochastic CFD and MHD problems.
300 $a 192 p.
500 $a Adviser: George Em Karniadakis.
500 $a Source: Dissertation Abstracts International, Volume: 68-07, Section: B, page: 4527.
502 $a Thesis (Ph.D.)--Brown University, 2007.
520 $a In computational fluid dynamics (CFD) and magneto-hydro-dynamics (MHD) applications there exist many sources of uncertainty, arising from imprecise material properties, random geometric roughness, noise in boundary/initial condition, transport coefficients, or external forcing. In this dissertation, stochastic perturbation analysis and stochastic simulations based on multi-element generalized polynomial chaos (ME-gPC) are employed synergistically, to solve large-scale stochastic CFD and MHD problems with many random inputs. Stochastic analytical solutions are obtained to serve in verifying the accuracy of the numerical results for small random inputs, but also in shedding light into the physical mechanisms and scaling laws associated with the structural changes of flow field due to random inputs.
520 $a First, the Karhuen-Loeve (K-L) decomposition is presented; it is an efficient technique for modeling the random inputs. How to represent the covariance kernel for different boundary constrains is an important issue. A new covariance matrix for an one-dimensional fourth-order random process with four boundary constraints is derived analytically, and it is used to model random rough wedge surfaces subjected to supersonic flow.
520 $a The algorithm of ME-gPC is presented next. ME-gPC is based on the decomposition of random space and spectral expansions. To efficiently solve complex stochastic fluid dynamical systems, e.g., stochastic compressible flows, the ME-gPC method is extended to multi-element probabilistic collocation method on sparse grids (ME-PCM) by coupling it with the probabilistic collocation projection. By using the sparse grid points, ME-PCM can handle random process with large number of random dimensions, with relative lower computational cost, compared to full tensor products. Several prototype problems in compressible and MHD flows are investigated by employing the aforementioned high-order stochastic numerical methods in conjunction with the stochastic perturbation analysis.
520 $a To handle complex systems with large number of random inputs, we also demonstrate how to couple sensitivity analysis and stochastic simulation together. Two MHD examples are presented to demonstrate the capability and efficiency of stochastic sensitivity analysis, which can be used as a pre-screening technique for reducing the dimensionality and hence the cost in large-scale stochastic simulations.
590 $a School code: 0024.
650 4 $a Applied Mechanics. $3 1018410
650 4 $a Engineering, Aerospace. $3 1018395
650 4 $a Mathematics. $3 515831
690 $a 0346
690 $a 0405
690 $a 0538
710 2 $a Brown University. $3 766761
773 0 $t Dissertation Abstracts International $g 68-07B.
790 $a 0024
790 1 0 $a Karniadakis, George Em, $e advisor
791 $a Ph.D.
792 $a 2007
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3272010