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Skeleton-stabilized IsoGeometric Analysis: High-regularity interior-penalty methods for incompressible viscous flow problems

机译：骨架稳定的等几何分析：用于不可压缩粘性流问题的高规则内部罚法

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摘要

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-alpha-regularity (0 = alpha k), only the derivative of order alpha + 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. (C) 2018 Elsevier B.V. All rights reserved.
机译：针对具有中等雷诺数的不可压缩粘性流动问题，提出了骨架稳定的等几何分析（SIGA）技术。所提出的方法允许利用相同的有限维空间（具有任意的B样条/ NURBS阶数和规则性）来近似压力和速度分量。关键思想是稳定变量的高阶导数在网格骨架上的跳跃。对于度数为k且具有C-alpha正则性（0 <= alpha

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