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09.12.2023 | Original Article

Stabilized isogeometric collocation methods for hyperbolic conservation laws

verfasst von: Ryan M. Aronson, John A. Evans

Erschienen in: Engineering with Computers | Ausgabe 6/2024

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Abstract

We introduce stabilized spline collocation schemes for the numerical solution of nonlinear, hyperbolic conservation laws. A nonlinear, residual-based viscosity stabilization is combined with a projection stabilization-inspired linear operator to stabilize the scheme in the presence of shocks and prevent the propagation of spurious, small-scale oscillations. Due to the nature of collocation schemes, these methods possess the possibility for greatly reduced computational cost of high-order discretizations. Numerical results for the linear advection, Burgers, Buckley–Leverett, and Euler equations show that the scheme is robust in the presence of shocks while maintaining high-order accuracy on smooth problems.

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Metadaten
Titel
Stabilized isogeometric collocation methods for hyperbolic conservation laws
verfasst von
Ryan M. Aronson
John A. Evans
Publikationsdatum
09.12.2023
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 6/2024
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-023-01918-4