The role of continuity in residual-based variational multiscale modeling of turbulence

By Ido Akkerman, Yuri Bazilevs, Victor Manuel Calo, Thomas J. R. Hughes, Sj Steven Hulshoff. 2007

243 citations recorded by the source corpus.

This paper examines the role of continuity of the basis in the computation of turbulent flows. We compare standard finite elements and non-uniform rational B-splines (NURBS) discretizations that are employed in Isogeometric Analysis (Hughes et al. in Comput Methods Appl Mech Eng, 194:4135–4195, 2005). We make use of quadratic discretizations that are C0-continuous across element boundaries in standard finite elements, and C1-continuous in the case of NURBS. The variational multiscale residual-based method (Bazilevs in Isogeometric analysis of turbulence and fluid-structure interaction, PhD thesis, ICES, UT Austin, 2006; Bazilevs et al. in Comput Methods Appl Mech Eng, submitted, 2007; Calo in Residual-based multiscale turbulence modeling: finite volume simulation of bypass transition. PhD thesis, Department of Civil and Environmental Engineering, Stanford University, 2004; Hughes et al. in proceedings of the XXI international congress of theoretical and applied mechanics (IUTAM), Kluwer, 2004; Scovazzi in Multiscale methods in science and engineering, PhD thesis, Department of Mechanical Engineering, Stanford Universty, 2004) is employed as a turbulence modeling technique. We find that C1-continuous discretizations outperform their C0-continuous counterparts on a per-degree-of-freedom basis. We also find that the effect of continuity is greater for higher Reynolds number flows.

Subfields: Computational Mechanics, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/086f9806b3f7c8c9dad96f8963e4564a136d9613

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Citations in the corpus

Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations (2010, methodology): “This method was originally derived in [18] for the equations of structural dynamics and subsequently applied to turbulence computations in [2,8,44] and to the Cahn-Hilliard phasefield model in [35,36].”
Large eddy simulation of turbulent Taylor-Couette flow using isogeometric analysis and the residual-based variational multiscale method (2010, background): “NURBS, due to their very good approximation properties and the ability to efficiently represent many engineering shapes exactly, are very well suited for turbulent flows [3,1] that also include rotating components [7].”
Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows (2007, result): “In a companion study we performed a comparison of NURBS and classical finite elements on turbulent channel flows, and the results confirmed our conjecture (see [1]).”
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 ”
Isogeometric collocation using analysis-suitable T-splines of arbitrary degree (2016, unknown): “, [12, 13, 14, 15, 16] and fluid-structure interaction (see, e.”
The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches (2010, background): “fluids, fluid-structure interaction, turbulence, phase field modeling, and structural optimization [3–19].”
A generalized finite element formulation for arbitrary basis functions: From isogeometric analysis to XFEM (2010, unknown): “Additional benefits may include higher order accuracy [2, 8, 9, 10, 11, 12, 13, 14], C(1) or higher continuity, and increased robustness [15].”
Isogeometric shell analysis: The Reissner-Mindlin shell (2010, unknown): “, [1,2,4–6,19,30,40]).”
Isogeometric analysis using T-splines (2010, methodology): “Isogeometric analysis of fluid flows with NURBS discretizations is a well-studied topic, with applications in turbulence modeling [2,5,9], cardiovascular flows [7,13,52], and fluid–structure interaction [6–8].”
Fast formation and assembly of finite element matrices with application to isogeometric linear elasticity (2019, background): “In particular, several investigations have demonstrated superior robustness and accuracy per degree of freedom [9, 30, 36], and excellent spectral behavior has been shown in a number of studies [19, 23, 31, 32] explaining the excellent results ob20 tained in applications such as structural dynamics ”
Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams (2016, methodology): “Over the last decade, IGA has become a well-established method used in a wide range of problems including structural mechanics [3–12] with recent developments for spatial Bernoulli beams [13,14], turbulent flow and fluid–structure interaction [15–20].”
Divergence-conforming discretization for Stokes problem on locally refined meshes using LR B-splines (2015, methodology): “7 Ξ = [1 , 3/2 2, 3 ] Ξ = [ 3/2, 2, 3, 3] Ξ = [1 , 2, 3, 3]”
NURBS-based isogeometric analysis for the computation of flows about rotating components (2008, unknown): “It should be noted that besides this geometrical advantage, NURBS discretizations were shown to produce more accurate results for incompressible flows as compared to standardfinite elements on a degree-of-freedom basis (see [ 1 ,5]).”
Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids (2011, result): “the results in [7–12]), it was found that NURBS-based isogeometric FEs give more accurate results than their traditional FE-counterparts.”