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arXiv · 1711.04910

Skeleton-stabilized IsoGeometric Analysis: High-regularity Interior-Penalty methods for incompressible viscous flow problems

Tuong Hoang·Clemens V. Verhoosel·Ferdinando Auricchio·E. Harald van Brummelen·Alessandro Reali
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Abstract

A Skeleton-stabilized IsoGeometric Analysis (SIGA) technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed method allows utilizing identical finite dimensional spaces (with arbitrary B-splines/NURBS order and regularity) for the approximation of the pressure and velocity components. The key idea is to stabilize the jumps of high-order derivatives of variables over the skeleton of the mesh. For B-splines/NURBS basis functions of degree $k$ with $C^α$-regularity ($0 \leq α< k$), only the derivative of order $α+1$ has to be controlled. This stabilization technique thus can be viewed as a high-regularity generalization of the (Continuous) Interior-Penalty Finite Element Method. Numerical experiments are performed for the Stokes and Navier-Stokes equations in two and three dimensions. Oscillation-free solutions and optimal convergence rates are obtained. In terms of the sparsity pattern of the algebraic system, we demonstrate that the block matrix associated with the stabilization term has a considerably smaller bandwidth when using B-splines than when using Lagrange basis functions, even in the case of $C^0$-continuity. This important property makes the proposed isogeometric framework practical from a computational effort point of view.

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Tuong Hoang, Clemens V. Verhoosel, Ferdinando Auricchio, E. Harald van Brummelen, Alessandro Reali. 2018-07-19. Skeleton-stabilized IsoGeometric Analysis: High-regularity Interior-Penalty methods for incompressible viscous flow problems. https://doi.org/10.1016/j.cma.2018.03.034

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