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Stabilized isogeometric collocation methods for hyperbolic conservation laws

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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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Authors and Affiliations

  1. Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, 94305, USA

    Ryan M. Aronson

  2. Ann and H. J. Smead Aerospace Engineering Sciences, University of Colorado Boulder, Boulder, CO, 80303, USA

    John A. Evans

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  1. Ryan M. Aronson
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Aronson, R.M., Evans, J.A. Stabilized isogeometric collocation methods for hyperbolic conservation laws. Engineering with Computers (2023). https://doi.org/10.1007/s00366-023-01918-4

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