Print Email Facebook Twitter Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. I: The convective–diffusive context Title Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. I: The convective–diffusive context Author ten Eikelder, M.F.P. (TU Delft Ship Hydromechanics and Structures) Akkerman, I. (TU Delft Ship Hydromechanics and Structures) Date 2018 Abstract This paper presents the construction of novel stabilized finite element methods in the convective–diffusive context that exhibit correct-energy behavior. Classical stabilized formulations can create unwanted artificial energy. Our contribution corrects this undesired property by employing the concepts of dynamic as well as orthogonal small-scales within the variational multiscale framework (VMS). The desire for correct energy indicates that the large- and small-scales should be H0 1-orthogonal. Using this orthogonality the VMS method can be converted into the streamline-upwind Petrov–Galerkin (SUPG) or the Galerkin/least-squares (GLS) method. Incorporating both large- and small-scales in the energy definition asks for dynamic behavior of the small-scales. Therefore, the large- and small-scales are treated as separate equations. Two consistent variational formulations which depict correct-energy behavior are proposed: (i) the Galerkin/least-squares method with dynamic small-scales (GLSD) and (ii) the dynamic orthogonal formulation (DO). The methods are presented in combination with an energy-decaying generalized-α time-integrator. Numerical verification shows that dissipation due to the small-scales in classical stabilized methods can become negative, on both a local and a global scale. The results show that without loss of accuracy the correct-energy behavior can be recovered by the proposed methods. The computations employ NURBS-based isogeometric analysis for the spatial discretization. Subject Correct-energy behaviorDynamic orthogonal small-scalesIsogeometric analysisResidual-based variational multiscale methodStabilized finite element methods To reference this document use: http://resolver.tudelft.nl/uuid:51505ede-0121-4b24-aebe-07d45193e3fc DOI https://doi.org/10.1016/j.cma.2017.11.020 Embargo date 2019-12-11 ISSN 0045-7825 Source Computer Methods in Applied Mechanics and Engineering, 331, 259-280 Bibliographical note Accepted Author Manuscript Part of collection Institutional Repository Document type journal article Rights © 2018 M.F.P. ten Eikelder, I. Akkerman Files PDF CD_Energy_revised_nocolor.pdf 2.57 MB Close viewer /islandora/object/uuid:51505ede-0121-4b24-aebe-07d45193e3fc/datastream/OBJ/view