Standard

A theoretical framework for discontinuity capturing : Joining variational multiscale analysis and variation entropy theory. / ten Eikelder, M. F.P.; Bazilevs, Y.; Akkerman, I.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 359, 112664, 2020.

Research output: Contribution to journalArticleScientificpeer-review

Harvard

APA

Vancouver

Author

BibTeX

@article{be5439f709a34ca38b44e1bc634a200d,
title = "A theoretical framework for discontinuity capturing: Joining variational multiscale analysis and variation entropy theory",
abstract = "In this paper we show that the variational multiscale method together with the variation entropy concept form the underlying theoretical framework of discontinuity capturing. The variation entropy [M.F.P. ten Eikelder and I. Akkerman, Comput. Methods Appl. Mech. Engrg. 355 (2019) 261-283] is the recently introduced concept that equips total variation diminishing solutions with an entropy foundation. This is the missing ingredient in order to show that the variational multiscale method can capture sharp layers. The novel framework naturally equips the variational multiscale method with a class of discontinuity capturing operators. This class includes the popular YZβ method and methods based on the residual of the variation-entropy. The discontinuity capturing mechanisms do not contain ad hoc devices and appropriate length scales are derived. Numerical results obtained with quadratic NURBS are virtually oscillation-free and show sharp layers, which confirms the viability of the methodology.",
keywords = "Discontinuity capturing operators, Isogeometric analysis, TVD property, Variation entropy, Variation entropy residual-based, Variational multiscale method",
author = "{ten Eikelder}, {M. F.P.} and Y. Bazilevs and I. Akkerman",
note = "Accepted Author Manuscript",
year = "2020",
doi = "10.1016/j.cma.2019.112664",
language = "English",
volume = "359",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - A theoretical framework for discontinuity capturing

T2 - Joining variational multiscale analysis and variation entropy theory

AU - ten Eikelder, M. F.P.

AU - Bazilevs, Y.

AU - Akkerman, I.

N1 - Accepted Author Manuscript

PY - 2020

Y1 - 2020

N2 - In this paper we show that the variational multiscale method together with the variation entropy concept form the underlying theoretical framework of discontinuity capturing. The variation entropy [M.F.P. ten Eikelder and I. Akkerman, Comput. Methods Appl. Mech. Engrg. 355 (2019) 261-283] is the recently introduced concept that equips total variation diminishing solutions with an entropy foundation. This is the missing ingredient in order to show that the variational multiscale method can capture sharp layers. The novel framework naturally equips the variational multiscale method with a class of discontinuity capturing operators. This class includes the popular YZβ method and methods based on the residual of the variation-entropy. The discontinuity capturing mechanisms do not contain ad hoc devices and appropriate length scales are derived. Numerical results obtained with quadratic NURBS are virtually oscillation-free and show sharp layers, which confirms the viability of the methodology.

AB - In this paper we show that the variational multiscale method together with the variation entropy concept form the underlying theoretical framework of discontinuity capturing. The variation entropy [M.F.P. ten Eikelder and I. Akkerman, Comput. Methods Appl. Mech. Engrg. 355 (2019) 261-283] is the recently introduced concept that equips total variation diminishing solutions with an entropy foundation. This is the missing ingredient in order to show that the variational multiscale method can capture sharp layers. The novel framework naturally equips the variational multiscale method with a class of discontinuity capturing operators. This class includes the popular YZβ method and methods based on the residual of the variation-entropy. The discontinuity capturing mechanisms do not contain ad hoc devices and appropriate length scales are derived. Numerical results obtained with quadratic NURBS are virtually oscillation-free and show sharp layers, which confirms the viability of the methodology.

KW - Discontinuity capturing operators

KW - Isogeometric analysis

KW - TVD property

KW - Variation entropy

KW - Variation entropy residual-based

KW - Variational multiscale method

UR - http://www.scopus.com/inward/record.url?scp=85073023780&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2019.112664

DO - 10.1016/j.cma.2019.112664

M3 - Article

AN - SCOPUS:85073023780

VL - 359

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

M1 - 112664

ER -

ID: 62173141