A Hybrid Finite Volume—Finite Element Method for Modeling Flows in Fractured Media View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2017

AUTHORS

Alexey Chernyshenko , Maxim Olshahskii , Yuri Vassilevski

ABSTRACT

Thiswork is devoted to the new hybrid method for solving a coupled system of advection–diffusion equations posed in a bulk domain and on an embedded surface. Systems of this kind arise in many engineering and natural science applications, but we consider the modeling of contaminant transport in fractured porous media as an example of an application. Fractures in a porous medium are considered as sharp interfaces between the surrounding bulk subdomains. The method is based on a monotone nonlinear finite volume scheme for equations posed in the bulk and a trace finite element method for equations posed on the surface. The surface is not fitted by the mesh and can cut through the background mesh in an arbitrary way. The background mesh is an octree grid with cubic cells. The surface intersects an octree grid and we get a polyhedral octree mesh with cut-cells. The numerical properties of the hybrid approach are illustrated in a series of numerical experiments with different embedded geometries. The method demonstrates great flexibility in handling curvilinear or branching embedded structures. More... »

PAGES

527-535

References to SciGraph publications

  • 2014. A Finite Volume Scheme with the Discrete Maximum Principle for Diffusion Equations on Polyhedral Meshes in FINITE VOLUMES FOR COMPLEX APPLICATIONS VII-METHODS AND THEORETICAL ASPECTS
  • Book

    TITLE

    Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems

    ISBN

    978-3-319-57393-9
    978-3-319-57394-6

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-57394-6_55

    DOI

    http://dx.doi.org/10.1007/978-3-319-57394-6_55

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1085572738


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0103", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Numerical and Computational Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Institute of Numerical Mathematics", 
              "id": "https://www.grid.ac/institutes/grid.465296.a", 
              "name": [
                "Institute of Numerical Mathematics"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Chernyshenko", 
            "givenName": "Alexey", 
            "id": "sg:person.016434506777.04", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016434506777.04"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Houston", 
              "id": "https://www.grid.ac/institutes/grid.266436.3", 
              "name": [
                "University of Houston"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Olshahskii", 
            "givenName": "Maxim", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Institute of Numerical Mathematics", 
              "id": "https://www.grid.ac/institutes/grid.465296.a", 
              "name": [
                "Institute of Numerical Mathematics"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Vassilevski", 
            "givenName": "Yuri", 
            "id": "sg:person.012104371362.91", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012104371362.91"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/978-3-319-05684-5_18", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004211110", 
              "https://doi.org/10.1007/978-3-319-05684-5_18"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1515/rnam-2012-0020", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025383669"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/nme.4823", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031474870"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.cma.2015.03.025", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040551875"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/080717602", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062854527"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2017", 
        "datePublishedReg": "2017-01-01", 
        "description": "Thiswork is devoted to the new hybrid method for solving a coupled system of advection\u2013diffusion equations posed in a bulk domain and on an embedded surface. Systems of this kind arise in many engineering and natural science applications, but we consider the modeling of contaminant transport in fractured porous media as an example of an application. Fractures in a porous medium are considered as sharp interfaces between the surrounding bulk subdomains. The method is based on a monotone nonlinear finite volume scheme for equations posed in the bulk and a trace finite element method for equations posed on the surface. The surface is not fitted by the mesh and can cut through the background mesh in an arbitrary way. The background mesh is an octree grid with cubic cells. The surface intersects an octree grid and we get a polyhedral octree mesh with cut-cells. The numerical properties of the hybrid approach are illustrated in a series of numerical experiments with different embedded geometries. The method demonstrates great flexibility in handling curvilinear or branching embedded structures.", 
        "editor": [
          {
            "familyName": "Canc\u00e8s", 
            "givenName": "Cl\u00e9ment", 
            "type": "Person"
          }, 
          {
            "familyName": "Omnes", 
            "givenName": "Pascal", 
            "type": "Person"
          }
        ], 
        "genre": "chapter", 
        "id": "sg:pub.10.1007/978-3-319-57394-6_55", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isFundedItemOf": [
          {
            "id": "sg:grant.6742307", 
            "type": "MonetaryGrant"
          }, 
          {
            "id": "sg:grant.4318344", 
            "type": "MonetaryGrant"
          }
        ], 
        "isPartOf": {
          "isbn": [
            "978-3-319-57393-9", 
            "978-3-319-57394-6"
          ], 
          "name": "Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems", 
          "type": "Book"
        }, 
        "name": "A Hybrid Finite Volume\u2014Finite Element Method for Modeling Flows in Fractured Media", 
        "pagination": "527-535", 
        "productId": [
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/978-3-319-57394-6_55"
            ]
          }, 
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "6bb7edfb5cf0d04cf61d663d24e281eae9ee653dee998dd69071b09f56bf0dfc"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1085572738"
            ]
          }
        ], 
        "publisher": {
          "location": "Cham", 
          "name": "Springer International Publishing", 
          "type": "Organisation"
        }, 
        "sameAs": [
          "https://doi.org/10.1007/978-3-319-57394-6_55", 
          "https://app.dimensions.ai/details/publication/pub.1085572738"
        ], 
        "sdDataset": "chapters", 
        "sdDatePublished": "2019-04-15T15:25", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8672_00000279.jsonl", 
        "type": "Chapter", 
        "url": "http://link.springer.com/10.1007/978-3-319-57394-6_55"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-57394-6_55'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-57394-6_55'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-57394-6_55'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-57394-6_55'


     

    This table displays all metadata directly associated to this object as RDF triples.

    106 TRIPLES      23 PREDICATES      32 URIs      20 LITERALS      8 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/978-3-319-57394-6_55 schema:about anzsrc-for:01
    2 anzsrc-for:0103
    3 schema:author N5d672464d5e94f41afea94767b184cc1
    4 schema:citation sg:pub.10.1007/978-3-319-05684-5_18
    5 https://doi.org/10.1002/nme.4823
    6 https://doi.org/10.1016/j.cma.2015.03.025
    7 https://doi.org/10.1137/080717602
    8 https://doi.org/10.1515/rnam-2012-0020
    9 schema:datePublished 2017
    10 schema:datePublishedReg 2017-01-01
    11 schema:description Thiswork is devoted to the new hybrid method for solving a coupled system of advection–diffusion equations posed in a bulk domain and on an embedded surface. Systems of this kind arise in many engineering and natural science applications, but we consider the modeling of contaminant transport in fractured porous media as an example of an application. Fractures in a porous medium are considered as sharp interfaces between the surrounding bulk subdomains. The method is based on a monotone nonlinear finite volume scheme for equations posed in the bulk and a trace finite element method for equations posed on the surface. The surface is not fitted by the mesh and can cut through the background mesh in an arbitrary way. The background mesh is an octree grid with cubic cells. The surface intersects an octree grid and we get a polyhedral octree mesh with cut-cells. The numerical properties of the hybrid approach are illustrated in a series of numerical experiments with different embedded geometries. The method demonstrates great flexibility in handling curvilinear or branching embedded structures.
    12 schema:editor N207188d136c44a7f87c44758f3c4b757
    13 schema:genre chapter
    14 schema:inLanguage en
    15 schema:isAccessibleForFree false
    16 schema:isPartOf Ne3b95077e97f40b381be1b77f0c61a6d
    17 schema:name A Hybrid Finite Volume—Finite Element Method for Modeling Flows in Fractured Media
    18 schema:pagination 527-535
    19 schema:productId N188734a4b449475fbdf8c1fcc267b6ed
    20 N4787322550234a468749487a382592f5
    21 N52b00b9c11c642c7a55ef8f3c3d45972
    22 schema:publisher Ndc8e3e6a7f6349608a253f047a078360
    23 schema:sameAs https://app.dimensions.ai/details/publication/pub.1085572738
    24 https://doi.org/10.1007/978-3-319-57394-6_55
    25 schema:sdDatePublished 2019-04-15T15:25
    26 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    27 schema:sdPublisher N6489347f58a540b0a733e35920ca8059
    28 schema:url http://link.springer.com/10.1007/978-3-319-57394-6_55
    29 sgo:license sg:explorer/license/
    30 sgo:sdDataset chapters
    31 rdf:type schema:Chapter
    32 N11f015cbca564666b4720544ecd178a6 rdf:first N77c334351cc44a809cc41847d061d11f
    33 rdf:rest rdf:nil
    34 N15a8fac6c1e74ad4bbb6865b54d7d4f9 rdf:first sg:person.012104371362.91
    35 rdf:rest rdf:nil
    36 N188734a4b449475fbdf8c1fcc267b6ed schema:name readcube_id
    37 schema:value 6bb7edfb5cf0d04cf61d663d24e281eae9ee653dee998dd69071b09f56bf0dfc
    38 rdf:type schema:PropertyValue
    39 N201071f017a44261b2eb419485e7b779 schema:familyName Cancès
    40 schema:givenName Clément
    41 rdf:type schema:Person
    42 N207188d136c44a7f87c44758f3c4b757 rdf:first N201071f017a44261b2eb419485e7b779
    43 rdf:rest N11f015cbca564666b4720544ecd178a6
    44 N4787322550234a468749487a382592f5 schema:name dimensions_id
    45 schema:value pub.1085572738
    46 rdf:type schema:PropertyValue
    47 N4e2ceda5a726425b855d5a773ab9f7ff rdf:first Ne737e23bef3441cbb61ed871d9aa00d2
    48 rdf:rest N15a8fac6c1e74ad4bbb6865b54d7d4f9
    49 N52b00b9c11c642c7a55ef8f3c3d45972 schema:name doi
    50 schema:value 10.1007/978-3-319-57394-6_55
    51 rdf:type schema:PropertyValue
    52 N5d672464d5e94f41afea94767b184cc1 rdf:first sg:person.016434506777.04
    53 rdf:rest N4e2ceda5a726425b855d5a773ab9f7ff
    54 N6489347f58a540b0a733e35920ca8059 schema:name Springer Nature - SN SciGraph project
    55 rdf:type schema:Organization
    56 N77c334351cc44a809cc41847d061d11f schema:familyName Omnes
    57 schema:givenName Pascal
    58 rdf:type schema:Person
    59 Ndc8e3e6a7f6349608a253f047a078360 schema:location Cham
    60 schema:name Springer International Publishing
    61 rdf:type schema:Organisation
    62 Ne3b95077e97f40b381be1b77f0c61a6d schema:isbn 978-3-319-57393-9
    63 978-3-319-57394-6
    64 schema:name Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems
    65 rdf:type schema:Book
    66 Ne737e23bef3441cbb61ed871d9aa00d2 schema:affiliation https://www.grid.ac/institutes/grid.266436.3
    67 schema:familyName Olshahskii
    68 schema:givenName Maxim
    69 rdf:type schema:Person
    70 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    71 schema:name Mathematical Sciences
    72 rdf:type schema:DefinedTerm
    73 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
    74 schema:name Numerical and Computational Mathematics
    75 rdf:type schema:DefinedTerm
    76 sg:grant.4318344 http://pending.schema.org/fundedItem sg:pub.10.1007/978-3-319-57394-6_55
    77 rdf:type schema:MonetaryGrant
    78 sg:grant.6742307 http://pending.schema.org/fundedItem sg:pub.10.1007/978-3-319-57394-6_55
    79 rdf:type schema:MonetaryGrant
    80 sg:person.012104371362.91 schema:affiliation https://www.grid.ac/institutes/grid.465296.a
    81 schema:familyName Vassilevski
    82 schema:givenName Yuri
    83 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012104371362.91
    84 rdf:type schema:Person
    85 sg:person.016434506777.04 schema:affiliation https://www.grid.ac/institutes/grid.465296.a
    86 schema:familyName Chernyshenko
    87 schema:givenName Alexey
    88 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016434506777.04
    89 rdf:type schema:Person
    90 sg:pub.10.1007/978-3-319-05684-5_18 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004211110
    91 https://doi.org/10.1007/978-3-319-05684-5_18
    92 rdf:type schema:CreativeWork
    93 https://doi.org/10.1002/nme.4823 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031474870
    94 rdf:type schema:CreativeWork
    95 https://doi.org/10.1016/j.cma.2015.03.025 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040551875
    96 rdf:type schema:CreativeWork
    97 https://doi.org/10.1137/080717602 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062854527
    98 rdf:type schema:CreativeWork
    99 https://doi.org/10.1515/rnam-2012-0020 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025383669
    100 rdf:type schema:CreativeWork
    101 https://www.grid.ac/institutes/grid.266436.3 schema:alternateName University of Houston
    102 schema:name University of Houston
    103 rdf:type schema:Organization
    104 https://www.grid.ac/institutes/grid.465296.a schema:alternateName Institute of Numerical Mathematics
    105 schema:name Institute of Numerical Mathematics
    106 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...