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 -