Intrusive methods in uncertainty quantification and their connection to kinetic theory

Intrusive methods in uncertainty quantification and their connection to kinetic theory Int J Adv Eng Sci Appl Math https://doi.org/10.1007/s12572-018-0211-3 IIT, Madras Intrusive methods in uncertainty quantification and their connection to kinetic theory 1 1 Jonas Kusch Martin Frank Indian Institute of Technology Madras 2018 Abstract Uncertainty quantification for hyperbolic equa- 1 Introduction tions is a challenging task, since solutions exhibit discon- tinuities and sharp gradients. The commonly used Today a lot of simulation applications make use of deter- stochastic-Galerkin (SG) Method uses polynomials to ministic models in order to predict the behavior of a represent the solution, leading to oscillatory approxima- physical system. Conservation equations are one prominent tions due to Gibbs phenomenon. Additionally, the SG example of such models and commonly lead to hyperbolic moment systems can loose hyperbolicity. The intrusive equations. Examples range from Euler equations in fluid polynomial moment method (IPMM) yields a general mechanics to the magnetohydrodynamics (MHD) equa- framework for intrusive methods while ensuring hyper- tions. However, the question arises whether these models bolicity of the moment system and restricting oscillatory allow a good investigation of the physical system in the over- and undershoots to specified bounds. In this contri- case of non-deterministic inputs. Deterministic inputs are bution, similarities as well as differences of the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Advances in Engineering Sciences and Applied Mathematics Springer Journals

Intrusive methods in uncertainty quantification and their connection to kinetic theory

Loading next page...
 
/lp/springer_journal/intrusive-methods-in-uncertainty-quantification-and-their-connection-sDiLBFJVAF
Publisher
Springer India
Copyright
Copyright © 2018 by Indian Institute of Technology Madras
Subject
Engineering; Engineering, general; Mathematical and Computational Engineering
ISSN
0975-0770
eISSN
0975-5616
D.O.I.
10.1007/s12572-018-0211-3
Publisher site
See Article on Publisher Site

Abstract

Int J Adv Eng Sci Appl Math https://doi.org/10.1007/s12572-018-0211-3 IIT, Madras Intrusive methods in uncertainty quantification and their connection to kinetic theory 1 1 Jonas Kusch Martin Frank Indian Institute of Technology Madras 2018 Abstract Uncertainty quantification for hyperbolic equa- 1 Introduction tions is a challenging task, since solutions exhibit discon- tinuities and sharp gradients. The commonly used Today a lot of simulation applications make use of deter- stochastic-Galerkin (SG) Method uses polynomials to ministic models in order to predict the behavior of a represent the solution, leading to oscillatory approxima- physical system. Conservation equations are one prominent tions due to Gibbs phenomenon. Additionally, the SG example of such models and commonly lead to hyperbolic moment systems can loose hyperbolicity. The intrusive equations. Examples range from Euler equations in fluid polynomial moment method (IPMM) yields a general mechanics to the magnetohydrodynamics (MHD) equa- framework for intrusive methods while ensuring hyper- tions. However, the question arises whether these models bolicity of the moment system and restricting oscillatory allow a good investigation of the physical system in the over- and undershoots to specified bounds. In this contri- case of non-deterministic inputs. Deterministic inputs are bution, similarities as well as differences of the

Journal

International Journal of Advances in Engineering Sciences and Applied MathematicsSpringer Journals

Published: Jun 1, 2018

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off