Lower-order refined preconditioning for spectral/hp element methods for complex, 3D geometries
File(s)ECCOMAS_CONGRESS_2024_Paper.pdf (1.97 MB)
Published version
Author(s)
Khurana, P
Sherwin, S
Hoessler, J
Moxey, D
Chatzopoulos, A
Type
Conference Paper
Abstract
The current work presents the incorporation of the Lower-Order Refined (LOR) preconditioner within the incompressible Navier-Stokes equations solver of the open-source spectral/hp element
method framework Nektar++. This preconditioner is constructed on a low-order (P=1) finite element
discretisation spectrally equivalent to a given high-order discretisation. The LOR preconditioner provides advantages like low cost operator evaluations, constant memory requirement per degree of freedom,
minimal sensitivity to high aspect-ratio elements and controlled iterative condition number with increasing problem size. The contribution extends to developing a functional LOR preconditioner tailored for
mixed-element 3D mesh configurations, encompassing both prismatic and tetrahedral elements, allowing
usage for complex geometries requiring unstructured 3D meshes with boundary layers. Notably, the
Nektar++ implementation is the first instance of using the LOR preconditioner with a modal expansion
basis function. This study presents the iterative performance and scaling of the proposed preconditioner
to solve the pressure Poisson system arising from the incompressible Navier-Stokes equations solver for
industrial test cases relevant to the context of race-car aerodynamics.
method framework Nektar++. This preconditioner is constructed on a low-order (P=1) finite element
discretisation spectrally equivalent to a given high-order discretisation. The LOR preconditioner provides advantages like low cost operator evaluations, constant memory requirement per degree of freedom,
minimal sensitivity to high aspect-ratio elements and controlled iterative condition number with increasing problem size. The contribution extends to developing a functional LOR preconditioner tailored for
mixed-element 3D mesh configurations, encompassing both prismatic and tetrahedral elements, allowing
usage for complex geometries requiring unstructured 3D meshes with boundary layers. Notably, the
Nektar++ implementation is the first instance of using the LOR preconditioner with a modal expansion
basis function. This study presents the iterative performance and scaling of the proposed preconditioner
to solve the pressure Poisson system arising from the incompressible Navier-Stokes equations solver for
industrial test cases relevant to the context of race-car aerodynamics.
Date Acceptance
2024-10-01
Citation
9th European Congress on Computational Methods in Applied Sciences and Engineering - Lisbon, 2024
Publisher
CIMNE
Journal / Book Title
9th European Congress on Computational Methods in Applied Sciences and Engineering - Lisbon, 2024
Copyright Statement
Copyright © 2024 The Author(s). This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License (https://creativecommons.org/licenses/by-nc-sa/4.0/).
Source
9th European Congress on Computational Methods in Applied Sciences and Engineering - Lisbon, 2024
Publication Status
Published
Start Date
2024-06-03
Finish Date
2024-06-07
Coverage Spatial
Lisbon, Portugal
Date Publish Online
2024-10-29