{"id":21044338,"url":"https://github.com/trixi-framework/paper-2024-generalized-upwind-sbp","last_synced_at":"2026-02-18T10:02:44.713Z","repository":{"id":244417832,"uuid":"814337711","full_name":"trixi-framework/paper-2024-generalized-upwind-sbp","owner":"trixi-framework","description":"Reproducibility repository for the paper \"Generalized upwind summation-by-parts operators and their application to nodal discontinuous Galerkin methods\"","archived":false,"fork":false,"pushed_at":"2025-02-19T08:30:25.000Z","size":1471,"stargazers_count":2,"open_issues_count":0,"forks_count":1,"subscribers_count":6,"default_branch":"main","last_synced_at":"2025-10-10T08:14:32.609Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":"","language":"Julia","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/trixi-framework.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":".zenodo.json","notice":null,"maintainers":null,"copyright":null,"agents":null,"dco":null,"cla":null}},"created_at":"2024-06-12T20:11:24.000Z","updated_at":"2025-02-28T02:56:38.000Z","dependencies_parsed_at":"2024-06-14T16:11:24.442Z","dependency_job_id":"3d787fbb-71fe-4b99-a072-2c349b014361","html_url":"https://github.com/trixi-framework/paper-2024-generalized-upwind-sbp","commit_stats":null,"previous_names":["trixi-framework/paper-2024-generalized-upwind-sbp"],"tags_count":2,"template":false,"template_full_name":null,"purl":"pkg:github/trixi-framework/paper-2024-generalized-upwind-sbp","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/trixi-framework%2Fpaper-2024-generalized-upwind-sbp","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/trixi-framework%2Fpaper-2024-generalized-upwind-sbp/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/trixi-framework%2Fpaper-2024-generalized-upwind-sbp/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/trixi-framework%2Fpaper-2024-generalized-upwind-sbp/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/trixi-framework","download_url":"https://codeload.github.com/trixi-framework/paper-2024-generalized-upwind-sbp/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/trixi-framework%2Fpaper-2024-generalized-upwind-sbp/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":29575343,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-02-18T08:38:15.585Z","status":"ssl_error","status_checked_at":"2026-02-18T08:38:14.917Z","response_time":162,"last_error":"SSL_read: unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":[],"created_at":"2024-11-19T14:16:22.355Z","updated_at":"2026-02-18T10:02:44.690Z","avatar_url":"https://github.com/trixi-framework.png","language":"Julia","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Generalized upwind summation-by-parts operators and their application to nodal discontinuous Galerkin methods\n\n[![License: MIT](https://img.shields.io/badge/License-MIT-success.svg)](https://opensource.org/licenses/MIT)\n[![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.11661785.svg)](https://doi.org/10.5281/zenodo.11661785)\n\nThis repository contains information and code to reproduce the results presented in the\narticle\n```bibtex\n@article{glaubitz2025generalized,\n  title={Generalized upwind summation-by-parts operators and their\n         application to nodal discontinuous {G}alerkin methods},\n  author={Glaubitz, Jan and Ranocha, Hendrik and Winters, Andrew Ross and\n          Schlottke-Lakemper, Michael and {\\\"O}ffner, Philipp and\n          Gassner, Gregor Josef},\n  journal={Journal of Computational Physics},\n  volume={529},\n  pages={113841},\n  year={2025},\n  month={05},\n  doi={10.1016/j.jcp.2025.113841},\n  eprint={2406.14557},\n  eprinttype={arxiv},\n  eprintclass={math.NA}\n}\n```\n\nIf you find these results useful, please cite the article mentioned above. If you\nuse the implementations provided here, please **also** cite this repository as\n```bibtex\n@misc{glaubitz2024generalizedRepro,\n  title={Reproducibility repository for\n         \"{G}eneralized upwind summation-by-parts operators and \n         their application to nodal discontinuous Galerkin methods\"},\n  author={Glaubitz, Jan and Ranocha, Hendrik and \n          Winters, Andrew Ross and Schlottke-Lakemper, Michael and \n          {\\\"O}ffner, Philipp and Gassner, Gregor Josef},\n  year={2024},\n  howpublished={\\url{https://github.com/trixi-framework/paper-2024-generalized-upwind-sbp}},\n  doi={10.5281/zenodo.11661785}\n}\n```\n\n## Abstract\n\nHigh-order numerical methods for conservation laws are highly sought after due to\ntheir potential efficiency. However, it is challenging to ensure their robustness,\nparticularly for under-resolved flows. Baseline high-order methods often incorporate\nstabilization techniques that must be applied judiciously—sufficient to ensure\nsimulation stability but restrained enough to prevent excessive dissipation and\nloss of resolution. Recent studies have demonstrated that combining upwind summation-by-parts (USBP)\noperators with flux vector splitting can increase the robustness of finite difference (FD)\nschemes without introducing excessive artificial dissipation. This work investigates whether\nthe same approach can be applied to nodal discontinuous Galerkin (DG) methods. To this end,\nwe demonstrate the existence of USBP operators on arbitrary grid points and provide\na straightforward procedure for their construction. Our discussion encompasses a\nbroad class of USBP operators, not limited to equidistant grid points, and enables\nthe development of novel USBP operators on Legendre–Gauss–Lobatto (LGL) points that are\nwell-suited for nodal DG methods. We then examine the robustness properties of the\nresulting DG-USBP methods for challenging examples of the compressible Euler equations,\nsuch as the Kelvin–Helmholtz instability. Similar to high-order FD-USBP schemes,\nwe find that combining flux vector splitting techniques with DG-USBP operators\ndoes not lead to excessive artificial dissipation. Furthermore, we find that\ncombining lower-order DG-USBP operators on three LGL points with flux vector splitting\nindeed increases the robustness of nodal DG methods. However, we also observe that\nhigher-order USBP operators offer less improvement in robustness for DG methods\ncompared to FD schemes. We provide evidence that this can be attributed to USBP methods\nadding dissipation only to unresolved modes, as FD schemes typically have more\nunresolved modes than nodal DG methods.\n\n\n## Numerical experiments\n\nThe numerical experiments presented in the paper use\n[Trixi.jl](https://github.com/trixi-framework/Trixi.jl).\nTo reproduce the numerical experiments using Trixi.jl, you need to install\n[Julia](https://julialang.org/).\n\nThe subfolder `code` of this repository contains a `README.md` file with\ninstructions to reproduce the Cartesian mesh numerical experiments and\nthe subfolder `code_curved` contains a `README.md` file with instructions\nto reproduce the curvilinear mesh numerical experiments.\n\nThe Cartesian mesh numerical experiments were carried out using Julia v1.9.4\nand the curvilinear mesh results were carried out using Julia 1.10.0.\n\n\n## Authors\n\n- [Jan Glaubitz](https://www.janglaubitz.com) (MIT, USA)\n- [Hendrik Ranocha](https://ranocha.de) (Johannes Gutenberg University Mainz, Germany)\n- [Andrew Winters](https://liu.se/en/employee/andwi94) (Linköping University, Sweden)\n- [Michael Schlottke-Lakemper](https://www.uni-augsburg.de/fakultaet/mntf/math/prof/hpsc) (University of Augsburg, Germany)\n- [Philipp Öffner](https://philippoeffner.de) (TU Clausthal, Germany)\n- [Gregor J. Gassner](https://www.mi.uni-koeln.de/NumSim/gregor-gassner/) (University of Cologne, Germany)\n\n\n## Disclaimer\n\nEverything is provided as is and without warranty. Use at your own risk!\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Ftrixi-framework%2Fpaper-2024-generalized-upwind-sbp","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Ftrixi-framework%2Fpaper-2024-generalized-upwind-sbp","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Ftrixi-framework%2Fpaper-2024-generalized-upwind-sbp/lists"}