A comparison of interpolation techniques for non-conformal high-order discontinuous Galerkin methods

Edward Laughton; Gavin Tabor; David Moxey

doi:10.1016/j.cma.2021.113820

A comparison of interpolation techniques for non-conformal high-order discontinuous Galerkin methods

Edward Laughton^*, Gavin Tabor, David Moxey

^*Corresponding author for this work

Engineering

University of Exeter

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

The capability to incorporate moving geometric features within models for complex simulations is a common requirement in many fields. Fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines, wheels and fan blades) or sliding components (e.g. in compressor or turbine cascade simulations). With an increasing trend towards the high-fidelity modelling of these cases, in particular combined with the use of high-order discontinuous Galerkin methods, there is therefore a requirement to understand how different numerical treatments of the interfaces between the static mesh and the sliding/rotating part impact on overall solution quality. In this article, we compare two different approaches to handle this non-conformal interface. The first is the so-called mortar approach, where flux integrals along edges are split according to the positioning of the non-conformal grid. The second is a less-documented point-to-point interpolation method, where the interior and exterior quantities for flux evaluations are interpolated from elements lying on the opposing side of the interface. Although the mortar approach has significant advantages in terms of its numerical properties, in that it preserves the local conservation properties of DG methods, in the context of complex 3D meshes it poses notable implementation difficulties which the point-to-point method handles more readily. In this paper we examine the numerical properties of each method, focusing not only on observing convergence orders for smooth solutions, but also how each method performs in under-resolved simulations of linear and nonlinear hyperbolic problems, to inform the use of these methods in implicit large-eddy simulations.

Original language	English
Article number	113820
Journal	COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume	381
DOIs	https://doi.org/10.1016/j.cma.2021.113820
Publication status	Published - 1 Aug 2021

Keywords

Mortar method
Moving geometry
Non-conformal mesh
Point-to-point interpolation
Spectral element method

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10.1016/j.cma.2021.113820

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title = "A comparison of interpolation techniques for non-conformal high-order discontinuous Galerkin methods",

abstract = "The capability to incorporate moving geometric features within models for complex simulations is a common requirement in many fields. Fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines, wheels and fan blades) or sliding components (e.g. in compressor or turbine cascade simulations). With an increasing trend towards the high-fidelity modelling of these cases, in particular combined with the use of high-order discontinuous Galerkin methods, there is therefore a requirement to understand how different numerical treatments of the interfaces between the static mesh and the sliding/rotating part impact on overall solution quality. In this article, we compare two different approaches to handle this non-conformal interface. The first is the so-called mortar approach, where flux integrals along edges are split according to the positioning of the non-conformal grid. The second is a less-documented point-to-point interpolation method, where the interior and exterior quantities for flux evaluations are interpolated from elements lying on the opposing side of the interface. Although the mortar approach has significant advantages in terms of its numerical properties, in that it preserves the local conservation properties of DG methods, in the context of complex 3D meshes it poses notable implementation difficulties which the point-to-point method handles more readily. In this paper we examine the numerical properties of each method, focusing not only on observing convergence orders for smooth solutions, but also how each method performs in under-resolved simulations of linear and nonlinear hyperbolic problems, to inform the use of these methods in implicit large-eddy simulations.",

keywords = "Mortar method, Moving geometry, Non-conformal mesh, Point-to-point interpolation, Spectral element method",

author = "Edward Laughton and Gavin Tabor and David Moxey",

note = "Funding Information: This work used the Isambard UK National Tier-2 HPC Service ( http://gw4.ac.uk/isambard/ ) operated by GW4 and the UK Met Office, and funded by EPSRC, UK under grant EP/P020224/1 . Funding Information: DM acknowledges support from the EPSRC Platform Grant PRISM under grant EP/R029423/1 and the ELEMENT project under grant EP/V001345/1 . Publisher Copyright: {\textcopyright} 2021 The Authors Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

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AU - Moxey, David

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PY - 2021/8/1

Y1 - 2021/8/1

N2 - The capability to incorporate moving geometric features within models for complex simulations is a common requirement in many fields. Fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines, wheels and fan blades) or sliding components (e.g. in compressor or turbine cascade simulations). With an increasing trend towards the high-fidelity modelling of these cases, in particular combined with the use of high-order discontinuous Galerkin methods, there is therefore a requirement to understand how different numerical treatments of the interfaces between the static mesh and the sliding/rotating part impact on overall solution quality. In this article, we compare two different approaches to handle this non-conformal interface. The first is the so-called mortar approach, where flux integrals along edges are split according to the positioning of the non-conformal grid. The second is a less-documented point-to-point interpolation method, where the interior and exterior quantities for flux evaluations are interpolated from elements lying on the opposing side of the interface. Although the mortar approach has significant advantages in terms of its numerical properties, in that it preserves the local conservation properties of DG methods, in the context of complex 3D meshes it poses notable implementation difficulties which the point-to-point method handles more readily. In this paper we examine the numerical properties of each method, focusing not only on observing convergence orders for smooth solutions, but also how each method performs in under-resolved simulations of linear and nonlinear hyperbolic problems, to inform the use of these methods in implicit large-eddy simulations.

AB - The capability to incorporate moving geometric features within models for complex simulations is a common requirement in many fields. Fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines, wheels and fan blades) or sliding components (e.g. in compressor or turbine cascade simulations). With an increasing trend towards the high-fidelity modelling of these cases, in particular combined with the use of high-order discontinuous Galerkin methods, there is therefore a requirement to understand how different numerical treatments of the interfaces between the static mesh and the sliding/rotating part impact on overall solution quality. In this article, we compare two different approaches to handle this non-conformal interface. The first is the so-called mortar approach, where flux integrals along edges are split according to the positioning of the non-conformal grid. The second is a less-documented point-to-point interpolation method, where the interior and exterior quantities for flux evaluations are interpolated from elements lying on the opposing side of the interface. Although the mortar approach has significant advantages in terms of its numerical properties, in that it preserves the local conservation properties of DG methods, in the context of complex 3D meshes it poses notable implementation difficulties which the point-to-point method handles more readily. In this paper we examine the numerical properties of each method, focusing not only on observing convergence orders for smooth solutions, but also how each method performs in under-resolved simulations of linear and nonlinear hyperbolic problems, to inform the use of these methods in implicit large-eddy simulations.

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KW - Moving geometry

KW - Non-conformal mesh

KW - Point-to-point interpolation

KW - Spectral element method

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JO - COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

JF - COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

M1 - 113820

ER -

A comparison of interpolation techniques for non-conformal high-order discontinuous Galerkin methods

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Keywords

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