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 -