2018/09/28 by Matthias Möller, Möller, Matthias, Jaeschke +1
Engineering · #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1809.10893
openalex publication_date 2018/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This work extends the high-resolution isogeometric analysis approach established for scalar transport equations 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 \citeKBNII. The underlying principles are reviewed and it is shown that linearized FCT-type flux limiting \citeKuzmin2009 originally derived for nodal low-order finite elements ensures positivity-preservation for high-order B-Spline discretizations.