Long-Term Behavior of Polynomial Chaos in Stochastic Flow Simulations

Abstract

In this paper we focus on the long-term behavior of generalized polynomial chaos (gPC) and multi-element generalized polynomial chaos (ME-gPC) for partial differential equations with stochastic coefficients. First, we consider the one-dimensional advection equation with a uniform random transport velocity and derive error estimates for gPC and ME-gPC discretizations. Subsequently, we extend these results to other random distributions and high-dimensional random inputs with numerical verification using the algebraic convergence rate of ME-gPC. Finally, we apply our results to noisy flow past a stationary circular cylinder. Simulation results demonstrate that ME-gPC is effective in improving the accuracy of gPC for a long-term integration whereas high-order gPC cannot capture the correct asymptotic behavior.

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Document Details

Document Type
Technical Report
Publication Date
Nov 23, 2005
Accession Number
ADA458983

Entities

People

  • George Karniadakis
  • Xiaoliang Wan

Organizations

  • Brown University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Applied Mathematics
  • Boundary Layer
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Flow
  • Frequency
  • Gaussian Distributions
  • Gaussian Processes
  • Mathematics
  • Navier Stokes Equations
  • Polynomials
  • Probability
  • Random Variables
  • Simulations
  • Stochastic Processes
  • Vortex Shedding

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematical Modeling and Probability Theory.
  • Positioning, Navigation, and Timing (PNT) Technology.