TY - GEN
T1 - High-Order Isogeometric Methods for Compressible Flows
T2 - 19th International Conference on Finite Elements in Flow Problems, FEF 2017
AU - Jaeschke, Andrzjeh
AU - Möller, Matthias
N1 - Accepted author manuscript
PY - 2020
Y1 - 2020
N2 - Isogeometric analysis was applied very successfully to many problem classes like linear elasticity, heat transfer and incompressible flow problems but its application to compressible flows is very rare. However, its ability to accurately represent complex geometries used in industrial applications makes IGA a suitable tool for the analysis of compressible flow problems that require the accurate resolution of boundary layers. The convection-diffusion solver presented in this chapter, is an indispensable step on the way to developing a compressible solver for complex viscous industrial flows. It is well known that the standard Galerkin finite element method and its isogeometric counterpart suffer from spurious oscillatory behaviour in the presence of shocks and steep solution gradients. As a remedy, the algebraic flux correction paradigm is generalized to B-Spline basis functions to suppress the creation of oscillations and occurrence of non-physical values in the solution. This work provides early results for scalar conservation laws and lays the foundation for extending this approach to the compressible Euler equations in the next chapter.
AB - Isogeometric analysis was applied very successfully to many problem classes like linear elasticity, heat transfer and incompressible flow problems but its application to compressible flows is very rare. However, its ability to accurately represent complex geometries used in industrial applications makes IGA a suitable tool for the analysis of compressible flow problems that require the accurate resolution of boundary layers. The convection-diffusion solver presented in this chapter, is an indispensable step on the way to developing a compressible solver for complex viscous industrial flows. It is well known that the standard Galerkin finite element method and its isogeometric counterpart suffer from spurious oscillatory behaviour in the presence of shocks and steep solution gradients. As a remedy, the algebraic flux correction paradigm is generalized to B-Spline basis functions to suppress the creation of oscillations and occurrence of non-physical values in the solution. This work provides early results for scalar conservation laws and lays the foundation for extending this approach to the compressible Euler equations in the next chapter.
KW - Algebraic flux correction
KW - Compressible flows
KW - Isogeometric analysis
UR - http://www.scopus.com/inward/record.url?scp=85081740195&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-30705-9_3
DO - 10.1007/978-3-030-30705-9_3
M3 - Conference contribution
AN - SCOPUS:85081740195
SN - 978-3-030-30704-2
T3 - Lecture Notes in Computational Science and Engineering
SP - 21
EP - 29
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 -