{
    "@context": [
        "https://www.researchobject.org/ro-crate/1.1/context.jsonld",
        "https://raw.githubusercontent.com/codemeta/codemeta/master/codemeta.jsonld"
    ],
    "@graph": [
        {
            "@id": "_:b0",
            "@type": "Grant",
            "funder": {
                "@id": "https://ror.org/05mmh0f86"
            },
            "identifier": "DP240102450"
        },
        {
            "@id": "_:b1",
            "@type": "Person",
            "familyName": "Mirko Velic"
        },
        {
            "@id": "_:b2",
            "@type": "PropertyValue",
            "propertyID": "oai",
            "value": "oai:zenodo.org:15128361"
        },
        {
            "@id": "http://example.org/base/",
            "@type": "Dataset",
            "about": {
                "@id": "https://linked.data.gov.au/def/anzsrc-for/2020/370401"
            },
            "abstract": "The accurate simulation of Earth's surface is essential for understanding lithospheric and mantle dynamics, especially in processes such as subduction and surface deformation. Traditional top boundary conditions, such as free-slip or no-slip, do not fully capture the complex interactions occurring at the surface. The commonly used \u201cSticky Air\u201d method, while practical, suffers from several limitations, including increased computational cost and marker fluctuation issues. Additionally, free surface numerical fluctuations, known as the \u201cdrunken sailor instability\u201d, are characteristic of all free surface simulations, including true Lagrangian free surface treatments and Arbitrary Lagrangian\u2013Eulerian (ALE) methods. In this study, we propose a novel scheme within the finite element framework that integrates the \u201cSticky Air\u201d concept into an ALE formulation by employing an internal boundary to simulate a true free surface, referred to as the ALE-IB. This approach effectively addresses the limitations of existing methods, notably by reducing marker fluctuation issues and enhancing numerical stability. Moreover, it maintains a true surface in the computational domain that can be further reshaped by surface processes such as erosion and deposition, and provides a foundational scheme for further coupling framework of tectonic modelling and landscape evolution modelling. We detail the theoretical formulation, implementation strategies, and validation through a series of numerical experiments. The results demonstrate that our method achieves higher accuracy and broader applicability compared to conventional techniques. Ultimately, this framework provides a more realistic and robust tool for geodynamic modelling of the Earth's free surface.",
            "creativeWorkStatus": "completed",
            "creator": {
                "@id": "https://orcid.org/0000-0001-9424-2315"
            },
            "isBasedOn": [],
            "spatialCoverage": "",
            "temporalCoverage": "",
            "alternateName": "Lu-2026-ALEIB-FreeSurface",
            "citation": {
                "@id": "https://doi.org/10.5194/gmd-19-5191-2026"
            },
            "contributor": [
                ""
            ],
            "creditText": [
                "Lu, N. (2026). A novel ALE scheme with the internal boundary for true free surface simulation in geodynamic models [Data set]. AuScope, National Computational Infrastructure. https://doi.org/qz3n-p243",
                ""
            ],
            "datePublished": "2026-09-09T01:54:03.000Z",
            "description": "We propose a novel scheme for modelling the true free surface within the finite element method (FEM), which integrates the \u201csticky air\u201d approach into the ALE scheme. This method employs an internal boundary to accurately represent the free surface, referred to as ALE-IB. We implement this scheme for free surface simulations in the geodynamic codes Underworld 2 and Underworld 3.",
            "funder": {
                "@id": "https://ror.org/05mmh0f86"
            },
            "funding": {
                "@id": "_:b0"
            },
            "hasPart": [
                {
                    "@id": "http://example.org/base/model_code_inputs"
                },
                {
                    "@id": "http://example.org/base/model_output_data"
                },
                {
                    "@id": "http://example.org/base/website_material"
                },
                {
                    "@id": "http://example.org/base/metadata_trail"
                },
                {
                    "@id": "http://example.org/base/#datasetCreation"
                },
                {
                    "@id": "http://example.org/base/landing_image"
                },
                {
                    "@id": "http://example.org/base/model_setup_figure"
                }
            ],
            "identifier": [
                "https://doi.org/10.25914/qz3n-p243"
            ],
            "isPartOf": "http://dx.doi.org/10.25914/yrzp-g882",
            "keywords": [
                "free surface",
                "ALE",
                "internal boundary"
            ],
            "license": "https://creativecommons.org/licenses/by/4.0/legalcode",
            "name": "A novel ALE scheme with the internal boundary for true free surface simulation in geodynamic models",
            "publisher": [
                {
                    "@id": "https://ror.org/04s1m4564"
                },
                {
                    "@id": "https://ror.org/04yx6dh41"
                }
            ],
            "url": [
                "https://mate.science/models/Lu-2026-ALEIB-FreeSurface/",
                "https://github.com/ModelAtlasofTheEarth/Lu-2026-ALEIB-FreeSurface/"
            ],
            "version": ""
        },
        {
            "@id": "http://example.org/base/#datasetCreation",
            "@type": "CreateAction",
            "agent": {
                "@id": "https://orcid.org/0000-0001-9424-2315"
            },
            "endTime": "",
            "instrument": [
                {
                    "@id": "https://doi.org/10.5281/zenodo.15128361"
                },
                {
                    "@id": "https://nci.org.au/"
                }
            ],
            "object": {
                "@id": "http://example.org/base/model_code_inputs"
            },
            "result": {
                "@id": "http://example.org/base/model_output_data"
            },
            "startTime": "",
            "description": "Running the computational model"
        },
        {
            "@id": "http://example.org/base/.metadata_trail",
            "@type": "Dataset",
            "hasPart": [
                {
                    "@id": "http://example.org/base/metadata_trail/issue_body.md"
                },
                {
                    "@id": "http://example.org/base/metadata_trail/issue_dict.json"
                },
                {
                    "@id": "http://example.org/base/metadata_trail/nci_iso.csv"
                },
                {
                    "@id": "http://example.org/base/metadata_trail/ro-crate-metadata-nested.json"
                }
            ],
            "name": ".metadata_trail"
        },
        {
            "@id": "http://example.org/base/.website_material",
            "@type": [
                "Dataset",
                "CreativeWork"
            ],
            "creator": {
                "@id": "https://orcid.org/0000-0001-9424-2315"
            },
            "fileFormat": "",
            "description": "material for m@te website",
            "name": ".website_material"
        },
        {
            "@id": "http://example.org/base/0000-0001-5865-1664",
            "@type": "Person",
            "familyName": "John Mansour"
        },
        {
            "@id": "http://example.org/base/0000-0001-6303-5671",
            "@type": "Person",
            "familyName": "Owen Kaluza"
        },
        {
            "@id": "http://example.org/base/0000-0001-7779-509X",
            "@type": "Person",
            "familyName": "Luke Mondy"
        },
        {
            "@id": "http://example.org/base/0000-0001-7919-2575",
            "@type": "Person",
            "familyName": "Ben Knight"
        },
        {
            "@id": "http://example.org/base/0000-0001-9424-2315",
            "@type": "Person",
            "familyName": "Neng Lu"
        },
        {
            "@id": "http://example.org/base/0000-0002-0368-7341",
            "@type": "Person",
            "familyName": "Steve Quenette"
        },
        {
            "@id": "http://example.org/base/0000-0002-1270-4377",
            "@type": "Person",
            "familyName": "Sara Mor\u00f3n"
        },
        {
            "@id": "http://example.org/base/0000-0002-1767-8593",
            "@type": "Person",
            "familyName": "Patrice Rey"
        },
        {
            "@id": "http://example.org/base/0000-0002-2207-6837",
            "@type": "Person",
            "familyName": "Dan Sandiford"
        },
        {
            "@id": "http://example.org/base/0000-0002-2594-6965",
            "@type": "Person",
            "familyName": "Rebecca Farrington"
        },
        {
            "@id": "http://example.org/base/0000-0002-3484-7985",
            "@type": "Person",
            "familyName": "Arijit Laik"
        },
        {
            "@id": "http://example.org/base/0000-0002-7182-1864",
            "@type": "Person",
            "familyName": "Adam Beall"
        },
        {
            "@id": "http://example.org/base/0000-0002-9512-7252",
            "@type": "Person",
            "familyName": "Guillaume Duclaux"
        },
        {
            "@id": "http://example.org/base/0000-0003-2595-2414",
            "@type": "Person",
            "familyName": "Claire Mallard"
        },
        {
            "@id": "http://example.org/base/0000-0003-3685-174X",
            "@type": "Person",
            "familyName": "Louis Moresi"
        },
        {
            "@id": "http://example.org/base/0000-0003-3891-5444",
            "@type": "Person",
            "familyName": "Romain Beucher"
        },
        {
            "@id": "http://example.org/base/0000-0003-4515-9296",
            "@type": "Person",
            "familyName": [
                "Giordani",
                "Julian Giordani"
            ],
            "givenName": "Julian"
        },
        {
            "@id": "http://example.org/base/landing_image",
            "@type": "ImageObject",
            "path": "https://raw.githubusercontent.com/ModelAtlasofTheEarth/Lu-2026-ALEIB-FreeSurface/update-mate2/.website_material/graphics/landing_image.png",
            "description": "Classification of methods used for simulating a free surface (indicated by the magenta line). Colored points represent markers for different materials. Methods include: (a) ALE scheme, (b) ALE scheme with the internal boundary (ALE-IB) and the \u201csticky air\u201d method, and (c) Eulerian scheme with the \u201csticky air\u201d method. The real interface refers to the actual free surface, while the virtual interface represents the surface obtained from numerical modelling.",
            "encodingFormat": "image/png",
            "name": "Landing page image"
        },
        {
            "@id": "http://example.org/base/metadata_trail/issue_body.md",
            "@type": "CreativeWork",
            "description": "Markdown document showing the original github issue body associated with the model submission.",
            "encodingFormat": "text/markdown",
            "name": "Issue Body"
        },
        {
            "@id": "http://example.org/base/metadata_trail/issue_dict.json",
            "@type": "CreativeWork",
            "description": "json file representing the dictionary that is constructured by model_submission/.github/scripts/parse_issue.py",
            "encodingFormat": "application/json",
            "name": "Issue Dictionary"
        },
        {
            "@id": "http://example.org/base/metadata_trail/nci_iso.csv",
            "@type": "CreativeWork",
            "description": "Simple crosswalk of metadata into ISO 19115 format/schema compatible with NCI GeoNwtework",
            "encodingFormat": "text/csv",
            "name": "NCI ISO Crosswalk"
        },
        {
            "@id": "http://example.org/base/metadata_trail/ro-crate-metadata-nested.json",
            "@type": "CreativeWork",
            "description": "Nested version of RO-Crate, hasn't been flattenened.",
            "encodingFormat": "application/json",
            "name": "Nested version of RO-Crate"
        },
        {
            "@id": "http://example.org/base/model_code_inputs",
            "@type": [
                "Dataset",
                "SoftwareSourceCode"
            ],
            "contentSize": "",
            "creator": "",
            "description": "Code and inputs for computational model",
            "identifier": [
                "https://doi.org/10.25914/qz3n-p243"
            ],
            "keywords": "",
            "memoryRequirements": "",
            "processorRequirements": "",
            "programmingLanguage": "",
            "runtimePlatform": "",
            "storageRequirements": "",
            "url": "https://thredds.nci.org.au/thredds/catalog/nm08/MATE/Lu-2026-ALEIB-FreeSurface/catalog.html",
            "version": ""
        },
        {
            "@id": "http://example.org/base/model_output_data",
            "@type": "Dataset",
            "contentSize": "",
            "creator": "",
            "fileFormat": "",
            "description": "",
            "identifier": [
                "https://doi.org/10.25914/qz3n-p243"
            ],
            "url": "https://thredds.nci.org.au/thredds/catalog/nm08/MATE/Lu-2026-ALEIB-FreeSurface/catalog.html"
        },
        {
            "@id": "http://example.org/base/model_setup_figure",
            "@type": "ImageObject",
            "path": "https://raw.githubusercontent.com/ModelAtlasofTheEarth/Lu-2026-ALEIB-FreeSurface/update-mate2/.website_material/graphics/model_setup_figure.png",
            "description": "Model setup for (a) viscous relaxation of sinusoidal topography, (b) Rayleigh\u2013Taylor instability, (c) delamination, (d) rising sphere, and (e) subduction. \u03a9 indicates different material domains, with \u03a90 specifically representing the air domain \u2013 used only in Eulerian and ALE-IB schemes. The dashed line marks the free surface, and the stars denote tracer locations used in some experiments.",
            "encodingFormat": "image/png",
            "name": "Model setup figure"
        },
        {
            "@id": "http://example.org/base/ro-crate-metadata.json",
            "@type": "CreativeWork",
            "conformsTo": {
                "@id": "https://w3id.org/ro/crate/1.1"
            },
            "about": {
                "@id": "http://example.org/base/"
            },
            "description": "RO-Crate Metadata File Descriptor (this file)"
        },
        {
            "@id": "https://creativecommons.org/licenses/by/4.0/legalcode",
            "@type": "CreativeWork",
            "description": "Creative Commons Attribution 4.0 International",
            "name": "CC-BY-4.0",
            "url": " https://creativecommons.org/licenses/by/4.0/legalcode.txt"
        },
        {
            "@id": "https://doi.org/10.5194/gmd-19-5191-2026",
            "@type": "ScholarlyArticle",
            "abstract": "Abstract. The accurate simulation of Earth's surface is essential for understanding lithospheric and mantle dynamics, especially in processes such as subduction and surface deformation. Traditional top boundary conditions, such as free-slip or no-slip, do not fully capture the complex interactions occurring at the surface. The commonly used \u201cSticky Air\u201d method, while practical, suffers from several limitations, including increased computational cost and marker fluctuation issues. Additionally, free surface numerical fluctuations, known as the \u201cdrunken sailor instability\u201d, are characteristic of all free surface simulations, including true Lagrangian free surface treatments and Arbitrary Lagrangian\u2013Eulerian (ALE) methods. In this study, we propose a novel scheme within the finite element framework that integrates the \u201cSticky Air\u201d concept into an ALE formulation by employing an internal boundary to simulate a true free surface, referred to as the ALE-IB. This approach effectively addresses the limitations of existing methods, notably by reducing marker fluctuation issues and enhancing numerical stability. Moreover, it maintains a true surface in the computational domain that can be further reshaped by surface processes such as erosion and deposition, and provides a foundational scheme for further coupling framework of tectonic modelling and landscape evolution modelling. We detail the theoretical formulation, implementation strategies, and validation through a series of numerical experiments. The results demonstrate that our method achieves higher accuracy and broader applicability compared to conventional techniques. Ultimately, this framework provides a more realistic and robust tool for geodynamic modelling of the Earth's free surface.",
            "author": [
                {
                    "@id": "https://orcid.org/0000-0001-9424-2315"
                },
                {
                    "@id": "https://orcid.org/0000-0003-3685-174X"
                },
                {
                    "@id": "http://example.org/base/0000-0003-4515-9296"
                }
            ],
            "name": "A novel ALE scheme with the internal boundary for true free surface simulation in geodynamic models"
        },
        {
            "@id": "https://doi.org/10.5281/zenodo.15128361",
            "@type": "SoftwareSourceCode",
            "author": [
                {
                    "@id": "http://example.org/base/0000-0003-3891-5444"
                },
                {
                    "@id": "http://example.org/base/0000-0003-4515-9296"
                },
                {
                    "@id": "http://example.org/base/0000-0003-3685-174X"
                },
                {
                    "@id": "http://example.org/base/0000-0001-5865-1664"
                },
                {
                    "@id": "http://example.org/base/0000-0001-6303-5671"
                },
                {
                    "@id": "_:b1"
                },
                {
                    "@id": "http://example.org/base/0000-0002-2594-6965"
                },
                {
                    "@id": "http://example.org/base/0000-0002-0368-7341"
                },
                {
                    "@id": "http://example.org/base/0000-0002-7182-1864"
                },
                {
                    "@id": "http://example.org/base/0000-0002-2207-6837"
                },
                {
                    "@id": "http://example.org/base/0000-0001-7779-509X"
                },
                {
                    "@id": "http://example.org/base/0000-0003-2595-2414"
                },
                {
                    "@id": "http://example.org/base/0000-0002-1767-8593"
                },
                {
                    "@id": "http://example.org/base/0000-0002-9512-7252"
                },
                {
                    "@id": "http://example.org/base/0000-0002-3484-7985"
                },
                {
                    "@id": "http://example.org/base/0000-0002-1270-4377"
                },
                {
                    "@id": "http://example.org/base/0000-0002-7182-1864"
                },
                {
                    "@id": "http://example.org/base/0000-0001-7919-2575"
                },
                {
                    "@id": "http://example.org/base/0000-0001-9424-2315"
                }
            ],
            "codeRepository": "https://github.com/underworldcode/underworld2",
            "identifier": {
                "@id": "_:b2"
            },
            "license": "https://www.gnu.org/licenses/lgpl-3.0-standalone.html",
            "name": "Underworld2, Underworld3",
            "url": "https://zenodo.org/doi/10.5281/zenodo.15128361"
        },
        {
            "@id": "https://linked.data.gov.au/def/anzsrc-for/2020/370401",
            "@type": "DefinedTerm",
            "termCode": "370401",
            "name": "Computational modelling and simulation in earth sciences"
        },
        {
            "@id": "https://nci.org.au/",
            "@type": "Service",
            "name": "",
            "url": "https://nci.org.au/"
        },
        {
            "@id": "https://orcid.org/0000-0001-9424-2315",
            "@type": "Person",
            "familyName": "Lu",
            "givenName": "Neng"
        },
        {
            "@id": "https://orcid.org/0000-0003-3685-174X",
            "@type": "Person",
            "familyName": "Moresi",
            "givenName": "Louis"
        },
        {
            "@id": "https://ror.org/04s1m4564",
            "@type": "Organization",
            "name": "AuScope"
        },
        {
            "@id": "https://ror.org/04yx6dh41",
            "@type": "Organization",
            "name": "National Computational Infrastructure"
        },
        {
            "@id": "https://ror.org/05mmh0f86",
            "@type": "Organization",
            "name": "ARC",
            "url": "https://www.arc.gov.au"
        }
    ]
}