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arXiv · 2306.00601

Stabilized Isogeometric Collocation Methods For Scalar Transport and Incompressible Fluid Flow

Ryan M. Aronson·Corey Wetterer-Nelson·John A. Evans
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Abstract

In this work we adapt classical residual-based stabilization techniques to the spline collocation setting. Inspired by the Streamline-Upwind-Petrov-Galerkin and Pressure-Stabilizing-Petrov-Galerkin methods, our stabilized collocation schemes address spurious oscillations that can arise from advection and pressure instabilities. Numerical examples for the advection-diffusion equation, Stokes equations, and incompressible Navier-Stokes equations show the effectiveness of the proposed stabilized schemes while maintaining the high-order convergence rates and accuracy of standard isogeometric collocation on smooth problems.

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Ryan M. Aronson, Corey Wetterer-Nelson, John A. Evans. 2023-06-01. Stabilized Isogeometric Collocation Methods For Scalar Transport and Incompressible Fluid Flow. https://arxiv.org/abs/2306.00601

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