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arXiv · 2307.07659

Stabilized Isogeometric Collocation Methods for Hyperbolic Conservation Laws

Ryan M. Aronson·John A. Evans
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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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Ryan M. Aronson, John A. Evans. 2023-07-14. Stabilized Isogeometric Collocation Methods for Hyperbolic Conservation Laws. https://arxiv.org/abs/2307.07659

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