Uncertainty quantification in computational fluid dynamics Hester Bijl, Didier Lucor, Siddhartha Mishra, Christoph Schwab, editors

Format:

Book

Contributor:

Bijl, Hester, editor.

Series:

Lecture notes in computational science and engineering ; 1439-7358 92

Lecture Notes in Computational Science and Engineering 1439-7358 92

Language:

English

Subjects (All):

Computational fluid dynamics.

Uncertainty--Mathematical models.

Uncertainty.

Mathematics.

Computational Mathematics and Numerical Analysis.

Computational Science and Engineering.

Appl. Mathematics/Computational Methods of Engineering.

Aerospace Technology and Astronautics.

Numerical and Computational Physics.

computer science.

data processing.

Local Subjects:

Mathematics.

Computational Mathematics and Numerical Analysis.

Computational Science and Engineering.

Appl. Mathematics/Computational Methods of Engineering.

Aerospace Technology and Astronautics.

Numerical and Computational Physics.

Physical Description:

1 online resource

Place of Publication:

Cham Springer 2013

Language Note:

English

System Details:

PDF

text file

Summary:

Fluid flows are characterized by uncertain inputs such as random initial data, material and flux coefficients, and boundary conditions. The current volume addresses the pertinent issue of efficiently computing the flow uncertainty, given this initial randomness. It collects seven original review articles that cover improved versions of the Monte Carlo method (the so-called multi-level Monte Carlo method (MLMC)), moment-based stochastic Galerkin methods and modified versions of the stochastic collocation methods that use adaptive stencil selection of the ENO-WENO type in both physical and stochastic space. The methods are also complemented by concrete applications such as flows around aerofoils and rockets, problems of aeroelasticity (fluid-structure interactions), and shallow water flows for propagating water waves. The wealth of numerical examples provide evidence on the suitability of each proposed method as well as comparisons of different approaches

Contents:

Non-intrusive Uncertainty Propagation with Error Bounds for Conservation Laws Containing Discontinuities Timothy Barth Uncertainty Quantification in Aeroelasticity Philip Beran and Bret Stanford Robust Uncertainty Propagation in Systems of Conservation Laws with the Entropy Closure Method Bruno Després, Gaël Poëtte and Didier Lucor Adaptive Uncertainty Quantification for Computational Fluid Dynamics Richard P. Dwight and Jeroen A.S. Witteveen Implementation of Intrusive Polynomial Chaos in CFD Codes and Application to 3D Navier-Stokes Chris Lacor and Cristian Dinescu Multi-level Monte Carlo Finite Volume Methods for Uncertainty Quantification in Nonlinear Systems of Balance Laws Siddhartha Mishra and Christoph Schwab Essentially Non-oscillatory Stencil Selection and Subcell Resolution in Uncertainty Quantification Jeroen A.S. Witteveen and Gianluca Iaccarino

5.2.1 Case of Euler System in Lagrangian Coordinates

5.3 Entropy Choice

5.4 Numerical Applications

5.4.1 Stochastic Riemann Problem for Euler Equations

5.4.2 Shock Hitting an Uncertain Interface Between Two Fluids

6 Parametric Uncertainty of the Model

6.1 First Case: The Model Parameter Is a Random Variable

6.1.1 Application to Uncertain γ-Law Gas Value

6.2 Second Case: The Model Parameter Is a Random Process

6.3 Modeling Parameter Uncertainties in Eulerian Systems

7 Conclusion and Open Problems

References

Adaptive Uncertainty Quantification for Computational Fluid Dynamics

1 Introduction

2 Method 1: Adaptive Stochastic Finite Elements with Newton-Cotes Quadrature

2.1 Background

2.2 Adaptive Stochastic Finite Elements

2.2.1 Newton-Cotes Quadrature in Simplex Elements

2.2.2 Stochastic Adaptive Grid Refinement

2.3 Numerical Results

2.3.1 Piston Problem

2.3.2 Transonic Flow over a NACA0012 Airfoil

3 Method 2: Gradient-Enhanced Kriging with Adaptivity for Uncertainty Quantification

3.1 Uncertainty Quantification Problem

3.2 Gradient Evaluation via the Adjoint Method

3.3 Gradient-Enhanced Kriging for Uncertainty Quantification

3.3.1 Kriging Response Surfaces

3.3.2 Gradient-Enhanced Kriging (GEK)

3.3.3 Adaptive Estimation of EA J

3.3.4 Implementation of Correlation Parameter Optimization

3.4 Limitations of Gradients for Response Surfaces in CFD

3.4.1 Oscillatory Gradients Due to Shocks

3.4.2 Gradient Error Due to a Frozen-Turbulence Approximation

3.5 Numerical Results

3.5.1 ``Sandtimer'' Model Problem

3.5.2 Piston Problem Redux

3.5.3 Shape Uncertainty for the RAE 2822 Aerofoil

Implementation of Intrusive Polynomial Chaos in CFD Codes and Application to 3D Navier-Stokes

2 Polynomial Chaos Methodology

Notes:

Includes bibliographical references

Online resource; title from PDF title page (SpringerLink, viewed September 24, 2013)

Other Format:

Print version Bijl, Hester. Uncertainty Quantification in Computational Fluid Dynamics

ISBN:

9783319008851

3319008854

3319008846

9783319008844

OCLC:

859778838

Access Restriction:

Restricted for use by site license