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Polynomial Chaos Methods for Hyperbolic Partial Differential EquationsLinear Transport Under Uncertainty

Polynomial Chaos Methods for Hyperbolic Partial Differential Equations: Linear Transport Under... [This chapter aims to present accurate and stable numerical schemes for the solution of a class of linear diffusive transport problems. The advection-diffusion equation subject to uncertain viscosity with known statistical description is represented by a spectral expansion in the stochastic dimension. The gPC framework and the stochastic Galerkin method are used to obtain an extended system which is analyzed to find discretization constraints on monotonicity, stiffness and stability. A comparison of stochastic Galerkin versus methods based on repeated evaluations of deterministic solutions, e.g., stochastic collocation, is not the primary focus of this chapter. However, we include a few examples on relative performance and numerical properties with respect to monotonicity requirements and convergence to steady-state, to encourage the use of stochastic Galerkin methods.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Polynomial Chaos Methods for Hyperbolic Partial Differential EquationsLinear Transport Under Uncertainty

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References (41)

Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2015
ISBN
978-3-319-10713-4
Pages
47 –80
DOI
10.1007/978-3-319-10714-1_5
Publisher site
See Chapter on Publisher Site

Abstract

[This chapter aims to present accurate and stable numerical schemes for the solution of a class of linear diffusive transport problems. The advection-diffusion equation subject to uncertain viscosity with known statistical description is represented by a spectral expansion in the stochastic dimension. The gPC framework and the stochastic Galerkin method are used to obtain an extended system which is analyzed to find discretization constraints on monotonicity, stiffness and stability. A comparison of stochastic Galerkin versus methods based on repeated evaluations of deterministic solutions, e.g., stochastic collocation, is not the primary focus of this chapter. However, we include a few examples on relative performance and numerical properties with respect to monotonicity requirements and convergence to steady-state, to encourage the use of stochastic Galerkin methods.]

Published: Sep 17, 2014

Keywords: Polynomial Chaos; Polynomial Chaos Expansion; Explicit Time Integration; Inviscid Limit; Stochastic Collocation

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