Hybrid discontinuous Galerkin-finite volume techniques for compressible flows on unstructured meshes

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dc.contributor.authorMaltsev, Vadim
dc.contributor.authorYuan, Dean
dc.contributor.authorJenkins, Karl W.
dc.contributor.authorSkote, Martin
dc.contributor.authorTsoutsanis, Panagiotis
dc.date.accessioned2022-11-14T11:26:18Z
dc.date.available2022-11-14T11:26:18Z
dc.date.issued2022-11-11
dc.description.abstractIn this paper we develop a family of arbitrarily high-order non-oscillatory hybrid Discontinuous Galerkin(DG)-Finite Volume(FV) schemes for mixed-element unstructured meshes. Their key ingredient is a switch between a DG method and a FV method based on the CWENOZ scheme when invalid solutions are detected by a troubled cell indicator checking the unlimited DG solution. Therefore, the high order of accuracy offered by DG is preserved in smooth regions of the computational domain, while the robustness of FV is utilized in regions with strong gradients. The high-order CWENOZ variant used has the same spatial order of accuracy as the DG variant, while representing one of the most compact applications on unstructured meshes, therefore simplifying the implementation, reducing the computational overhead associated with large stencils of the original WENO reconstruction without sacrificing the desirable non-oscillatory properties of the schemes. We carefully investigate several parameters associated with the switching between DG and FV methods including the troubled cell indicators in a priori fashion. For the first time in the literature, we investigate the definition of the bounds for an admissible solution, the frequency by which we use the troubled cell indicators, and the evolution of the percentage of troubled cells for unsteady test problems. The 2D and 3D Euler equations are solved for well established test problems and compared with computational or experimental reference solutions. All the methods have been implemented and deployed within the UCNS3D open-source high-order unstructured Computational Fluid Dynamics (CFD) solver. The present coupling has the potential to improve the shortcomings of both FV-DG in a computational efficient manner. The improved accuracy and robustness provided is a characteristic of paramount importance for industrial-scale CFD applications, and favours the extension to other systems of governing equations.en_UK
dc.identifier.citationMaltsev V, Yuan D, Jenkins KW, et al., (2023) Hybrid discontinuous Galerkin-finite volume techniques for compressible flows on unstructured meshes. Journal of Computational Physics, Volume 473, January 2023, Article number 111755en_UK
dc.identifier.issn0021-9991
dc.identifier.urihttps://doi.org/10.1016/j.jcp.2022.111755
dc.identifier.urihttps://dspace.lib.cranfield.ac.uk/handle/1826/18705
dc.language.isoenen_UK
dc.publisherElsevieren_UK
dc.rightsAttribution 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subjectHybrid DG-FVen_UK
dc.subjectUnstructured meshesen_UK
dc.subjectTroubled cell indicatorsen_UK
dc.subjectSupersonic civil airlineren_UK
dc.subjectUCNS3Den_UK
dc.titleHybrid discontinuous Galerkin-finite volume techniques for compressible flows on unstructured meshesen_UK
dc.typeArticleen_UK

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