TY - GEN

T1 - High-Order Isogeometric Methods for Compressible Flows

T2 - 19th International Conference on Finite Elements in Flow Problems, FEF 2017

AU - Möller, Matthias

AU - Jaeschke, Andrzjeh

N1 - Accepted author manuscript

PY - 2020

Y1 - 2020

N2 - This work extends the high-resolution isogeometric analysis approach established in chapter “High-Order Isogeometric Methods for Compressible Flows. I: Scalar Conservation Laws” (Jaeschke and Möller: High-order isogeometric methods for compressible flows. I. Scalar conservation Laws. In: Proceedings of the 19th International Conference on Finite Elements in Flow Problems (FEF 2017)) to the equations of gas dynamics. The group finite element formulation is adopted to obtain an efficient assembly procedure for the standard Galerkin approximation, which is stabilized by adding artificial viscosities proportional to the spectral radius of the Roe-averaged flux-Jacobian matrix. Excess stabilization is removed in regions with smooth flow profiles with the aid of algebraic flux correction (Kuzmin et al., Flux-corrected transport, chapter Algebraic flux correction II. Compressible Flow Problems. Springer, Berlin, 2012). The underlying principles are reviewed and it is shown that linearized FCT-type flux limiting (Kuzmin, J Comput Phys 228(7):2517–2534, 2009) originally derived for nodal low-order finite elements ensures positivity-preservation for high-order B-Spline discretizations.

AB - This work extends the high-resolution isogeometric analysis approach established in chapter “High-Order Isogeometric Methods for Compressible Flows. I: Scalar Conservation Laws” (Jaeschke and Möller: High-order isogeometric methods for compressible flows. I. Scalar conservation Laws. In: Proceedings of the 19th International Conference on Finite Elements in Flow Problems (FEF 2017)) to the equations of gas dynamics. The group finite element formulation is adopted to obtain an efficient assembly procedure for the standard Galerkin approximation, which is stabilized by adding artificial viscosities proportional to the spectral radius of the Roe-averaged flux-Jacobian matrix. Excess stabilization is removed in regions with smooth flow profiles with the aid of algebraic flux correction (Kuzmin et al., Flux-corrected transport, chapter Algebraic flux correction II. Compressible Flow Problems. Springer, Berlin, 2012). The underlying principles are reviewed and it is shown that linearized FCT-type flux limiting (Kuzmin, J Comput Phys 228(7):2517–2534, 2009) originally derived for nodal low-order finite elements ensures positivity-preservation for high-order B-Spline discretizations.

KW - Compressible flows

KW - High-order methods

KW - High-resolution methods

KW - Isogeometric analysis

UR - http://www.scopus.com/inward/record.url?scp=85081751206&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-30705-9_4

DO - 10.1007/978-3-030-30705-9_4

M3 - Conference contribution

AN - SCOPUS:85081751206

SN - 978-3-030-30704-2

T3 - Lecture Notes in Computational Science and Engineering

SP - 31

EP - 39

BT - Numerical Methods for Flows - FEF 2017 Selected Contributions

A2 - van Brummelen, Harald

A2 - Corsini, Alessandro

A2 - Perotto, Simona

A2 - Rozza, Gianluigi

PB - Springer

CY - Cham

Y2 - 5 April 2017 through 7 April 2017

ER -