Stabilized Isogeometric Collocation Methods for Hyperbolic Conservation Laws
Numerical Analysis
2023-07-18 v1 Numerical Analysis
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.
Cite
@article{arxiv.2307.07659,
title = {Stabilized Isogeometric Collocation Methods for Hyperbolic Conservation Laws},
author = {Ryan M. Aronson and John A. Evans},
journal= {arXiv preprint arXiv:2307.07659},
year = {2023}
}