Print Email Facebook Twitter Construction and application of an algebraic dual basis and the Fine-Scale Greens’ Function for computing projections and reconstructing unresolved scales Title Construction and application of an algebraic dual basis and the Fine-Scale Greens’ Function for computing projections and reconstructing unresolved scales Author Shrestha, S. (TU Delft Aerodynamics; Universidad Politécnica de Madrid) Dekker, J. (TU Delft Numerical Analysis) Gerritsma, M.I. (TU Delft Aerodynamics) Hulshoff, S.J. (TU Delft Aerodynamics) Akkerman, I. (TU Delft Ship Hydromechanics and Structures) Date 2024 Abstract In this paper, we build on the work of Hughes and Sangalli (2007) dealing with the explicit computation of the Fine-Scale Greens’ function. The original approach chooses a set of functionals associated with a projector to compute the Fine-Scale Greens’ function. The construction of these functionals, however, does not generalise to arbitrary projections, higher dimensions, or Spectral Element methods. We propose to generalise the construction of the required functionals by using dual functions. These dual functions can be directly derived from the chosen projector and are explicitly computable. We show how to find the dual functions for both the L2 and the H01 projections. We then go on to demonstrate that the Fine-Scale Greens’ functions constructed with the dual basis functions consistently reproduce the unresolved scales removed by the projector. The methodology is tested using one-dimensional Poisson and advection–diffusion problems, as well as a two-dimensional Poisson problem. We present the computed components of the Fine-Scale Greens’ function, and the Fine-Scale Greens’ function itself. These results show that the method works for arbitrary projections, in arbitrary dimensions. Moreover, the methodology can be applied to any Finite/Spectral Element or Isogeometric framework. Subject (Fine-Scale) Greens’ functionAdvection–diffusion equationDualityPoisson equationProjectionVariational multiscale To reference this document use: http://resolver.tudelft.nl/uuid:e731427f-24d4-4e2d-a24a-4dc46ebf7972 DOI https://doi.org/10.1016/j.cma.2024.116833 ISSN 0045-7825 Source Computer Methods in Applied Mechanics and Engineering, 422 Part of collection Institutional Repository Document type journal article Rights © 2024 S. Shrestha, J. Dekker, M.I. Gerritsma, S.J. Hulshoff, I. Akkerman Files PDF 1-s2.0-S0045782524000896-main.pdf 3.16 MB Close viewer /islandora/object/uuid:e731427f-24d4-4e2d-a24a-4dc46ebf7972/datastream/OBJ/view