Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations

By Hector Gomez, Thomas J. R. Hughes, Xesús Nogueira, Victor Manuel Calo. 2010

254 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/e37b1dfb5ecff039de0de9d9d3d8ff0731c87819

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In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

An unconditionally energy-stable method for the phase field crystal equation (2012, methodology): “Even more importantly for the present work, the use of NURBS permits generating globally C-continuous basis functions easily, which leads to a simple and efficient discretization of higher-order operators as shown in [25–28].”
The variational collocation method (2016, methodology): “The higher-order continuity of the basis functions used in IGA (among other advantages [7, 8, 9, 10]) allows for a straightforward application of the collocation method, while retaining the geometric flexibility of finite elements [11, 12, 13].”
Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS (2012, background): “Extensive investigations including fluid–solid interaction [3,2], the extended finite element method [5] and electromagnetics [8] have additionally demonstrated the ability of isogeometric analysis to provide not only more precise geometric representations than traditional finite elements but also e”
Isogeometric collocation using analysis-suitable T-splines of arbitrary degree (2016, unknown): “, [12, 13, 14, 15, 16] and fluid-structure interaction (see, e.”
Local refinement of analysis-suitable T-splines (2012, methodology): “Areas of application of NURBS-based isogeometric analysis include turbulence [5–8], fluid–structure interaction [9–12], incompressibility [13–15], structural analysis [16,3], plates and shells [17–21], phase-field analysis [22,23], large deformation with mesh distortion [24], shape optimization [25–”
Phase-field modeling of fracture in linear thin shells (2014, unknown): “Phase-field methods are widely used in science and engineering to model a variety of physics [23, 24, 25, 26].”
Isogeometric discretizations of the Stokes problem: stability analysis by the macroelement technique (2013, methodology): “This technique is having a growing impact on several fields, from fluid dynamics (Bazilevs et al., 2007, 2008, 2010; Zhang et al., 2007; Gomez et al., 2010; Buffa et al., 2011) to structural mechanics (Cottrell et al.”
Isogeometric analysis: An overview and computer implementation aspects (2012, background): “The smoothness of NURBS basis functions is attractive for analysis of fluids [7, 53, 96] and for fluid-structure interaction problems [9, 10].”
Isogeometric boundary element analysis using unstructured T-splines (2013, methodology): “A small sampling includes fluids and turbulence [5, 6, 7, 8], fluid-structure interaction [9, 10, 11, 12], incompressibility [13, 14, 15], structural and vibration analysis [16, 3], plates and shells [17, 18, 19, 20, 21], phase-field analysis [22, 23, 24], large deformation structural analysis with ”
A NURBS-based immersed methodology for fluid–structure interaction (2015, methodology): “If we compare NURBS with Lagrange functions, which are typically used in the finite element method, NURBS have several advantages due to their higher continuity between elements and some of them are the following: First, spatial derivatives of second or higher order may be computed easily, which per”