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 -