Grid convergence for numerical solutions of stochastic moment equations of groundwater flow View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-09-05

AUTHORS

Chuan-An Xia, Alberto Guadagnini, Bill X. Hu, Monica Riva, Philippe Ackerer

ABSTRACT

We provide qualitative and quantitative assessment of the results of a grid convergence study in terms of (a) the rate/order of convergence and (b) the grid convergence index, GCI, associated with the numerical solutions of moment equations (MEs) of steady-state groundwater flow. The latter are approximated at second order (in terms of the standard deviation of the natural logarithm, Y, of hydraulic conductivity). We consider (1) the analytical solutions of Riva et al. (Transp Porous Med 45(1):139–193, 2001) for steady-state radial flow in a randomly heterogeneous conductivity field, which we take as references; and (2) the numerical solutions of the MEs satisfied by the (ensemble) mean and (co)variance of hydraulic head and fluxes. Based on 45 numerical grids associated with differing degrees of discretization, we find a supra-linear rate of convergence for the mean and (co)variance of hydraulic head and for the variance of the transverse component of fluxes, the variance of radial fluxes being characterized by a sub-linear convergence rate. Our estimated values of GCI suggest that an accurate computation of mean and (co)variance of head and fluxes requires a space discretization comprising at least 8 grid elements per correlation length of Y, an even finer discretization being required for an accurate representation of the second-order component of mean heads. More... »

PAGES

1565-1579

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00477-019-01719-6

DOI

http://dx.doi.org/10.1007/s00477-019-01719-6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1120876362


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/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "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"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Institute of Groundwater and Earth Science, Jinan University, 510632, Guangzhou, China", 
          "id": "http://www.grid.ac/institutes/grid.258164.c", 
          "name": [
            "Institute of Groundwater and Earth Science, Jinan University, 510632, Guangzhou, China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Xia", 
        "givenName": "Chuan-An", 
        "id": "sg:person.012527715750.15", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012527715750.15"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Hydrology and Atmospheric Sciences, The University of Arizona, Tucson, USA", 
          "id": "http://www.grid.ac/institutes/grid.134563.6", 
          "name": [
            "Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Milan, Italy", 
            "Department of Hydrology and Atmospheric Sciences, The University of Arizona, Tucson, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Guadagnini", 
        "givenName": "Alberto", 
        "id": "sg:person.01337311443.28", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01337311443.28"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Institute of Groundwater and Earth Science, Jinan University, 510632, Guangzhou, China", 
          "id": "http://www.grid.ac/institutes/grid.258164.c", 
          "name": [
            "Institute of Groundwater and Earth Science, Jinan University, 510632, Guangzhou, China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Hu", 
        "givenName": "Bill X.", 
        "id": "sg:person.012556140447.41", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012556140447.41"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Hydrology and Atmospheric Sciences, The University of Arizona, Tucson, USA", 
          "id": "http://www.grid.ac/institutes/grid.134563.6", 
          "name": [
            "Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Milan, Italy", 
            "Department of Hydrology and Atmospheric Sciences, The University of Arizona, Tucson, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Riva", 
        "givenName": "Monica", 
        "id": "sg:person.013140342153.18", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013140342153.18"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "CNRS, Lab Hydrol & Geochim Strasbourg, Univ Strasbourg, 1 Rue Blessig, 67084, Strasbourg, France", 
          "id": "http://www.grid.ac/institutes/grid.11843.3f", 
          "name": [
            "Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Milan, Italy", 
            "CNRS, Lab Hydrol & Geochim Strasbourg, Univ Strasbourg, 1 Rue Blessig, 67084, Strasbourg, France"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Ackerer", 
        "givenName": "Philippe", 
        "id": "sg:person.011325456565.14", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011325456565.14"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/s00477-005-0023-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043846797", 
          "https://doi.org/10.1007/s00477-005-0023-4"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1023/a:1011880602668", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008657512", 
          "https://doi.org/10.1023/a:1011880602668"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00477-003-0154-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048479377", 
          "https://doi.org/10.1007/s00477-003-0154-4"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1023/a:1022277418570", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1036663944", 
          "https://doi.org/10.1023/a:1022277418570"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00477-003-0161-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030430208", 
          "https://doi.org/10.1007/s00477-003-0161-5"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2019-09-05", 
    "datePublishedReg": "2019-09-05", 
    "description": "We provide qualitative and quantitative assessment of the results of a grid convergence study in terms of (a) the rate/order of convergence and (b) the grid convergence index, GCI, associated with the numerical solutions of moment equations (MEs) of steady-state groundwater flow. The latter are approximated at second order (in terms of the standard deviation of the natural logarithm, Y, of hydraulic conductivity). We consider (1) the analytical solutions of Riva et al. (Transp Porous Med 45(1):139\u2013193, 2001) for steady-state radial flow in a randomly heterogeneous conductivity field, which we take as references; and (2) the numerical solutions of the MEs satisfied by the (ensemble) mean and (co)variance of hydraulic head and fluxes. Based on 45 numerical grids associated with differing degrees of discretization, we find a supra-linear rate of convergence for the mean and (co)variance of hydraulic head and for the variance of the transverse component of fluxes, the variance of radial fluxes being characterized by a sub-linear convergence rate. Our estimated values of GCI suggest that an accurate computation of mean and (co)variance of head and fluxes requires a space discretization comprising at least 8 grid elements per correlation length of Y, an even finer discretization being required for an accurate representation of the second-order component of mean heads.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/s00477-019-01719-6", 
    "inLanguage": "en", 
    "isAccessibleForFree": true, 
    "isFundedItemOf": [
      {
        "id": "sg:grant.8277564", 
        "type": "MonetaryGrant"
      }, 
      {
        "id": "sg:grant.8231944", 
        "type": "MonetaryGrant"
      }
    ], 
    "isPartOf": [
      {
        "id": "sg:journal.1039987", 
        "issn": [
          "1436-3240", 
          "1436-3259"
        ], 
        "name": "Stochastic Environmental Research and Risk Assessment", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "8-9", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "33"
      }
    ], 
    "keywords": [
      "moment equations", 
      "numerical solution", 
      "sub-linear convergence rate", 
      "stochastic moment equations", 
      "degree of discretization", 
      "grid convergence study", 
      "heterogeneous conductivity fields", 
      "steady-state groundwater flow", 
      "steady-state radial flow", 
      "grid convergence index", 
      "space discretization", 
      "conductivity field", 
      "grid convergence", 
      "fine discretization", 
      "convergence rate", 
      "accurate computation", 
      "second order", 
      "numerical grid", 
      "analytical solution", 
      "correlation length", 
      "discretization", 
      "convergence study", 
      "mean head", 
      "groundwater flow", 
      "hydraulic head", 
      "transverse components", 
      "grid elements", 
      "convergence", 
      "convergence index", 
      "equations", 
      "radial flux", 
      "second-order components", 
      "radial flow", 
      "accurate representation", 
      "solution", 
      "flow", 
      "computation", 
      "flux", 
      "grid", 
      "field", 
      "variance", 
      "representation", 
      "order", 
      "means", 
      "GCI", 
      "terms", 
      "al", 
      "quantitative assessment", 
      "components", 
      "results", 
      "elements", 
      "values", 
      "length", 
      "reference", 
      "degree", 
      "rate", 
      "index", 
      "study", 
      "head", 
      "assessment", 
      "Rivas", 
      "rate/order", 
      "supra-linear rate", 
      "values of GCI"
    ], 
    "name": "Grid convergence for numerical solutions of stochastic moment equations of groundwater flow", 
    "pagination": "1565-1579", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1120876362"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s00477-019-01719-6"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s00477-019-01719-6", 
      "https://app.dimensions.ai/details/publication/pub.1120876362"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-01-01T18:49", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/article/article_814.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/s00477-019-01719-6"
  }
]
 

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/s00477-019-01719-6'

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/s00477-019-01719-6'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00477-019-01719-6'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00477-019-01719-6'


 

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

182 TRIPLES      22 PREDICATES      94 URIs      81 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s00477-019-01719-6 schema:about anzsrc-for:01
2 anzsrc-for:0103
3 schema:author Ncaf9683a280244069f7e0161f9387ff1
4 schema:citation sg:pub.10.1007/s00477-003-0154-4
5 sg:pub.10.1007/s00477-003-0161-5
6 sg:pub.10.1007/s00477-005-0023-4
7 sg:pub.10.1023/a:1011880602668
8 sg:pub.10.1023/a:1022277418570
9 schema:datePublished 2019-09-05
10 schema:datePublishedReg 2019-09-05
11 schema:description We provide qualitative and quantitative assessment of the results of a grid convergence study in terms of (a) the rate/order of convergence and (b) the grid convergence index, GCI, associated with the numerical solutions of moment equations (MEs) of steady-state groundwater flow. The latter are approximated at second order (in terms of the standard deviation of the natural logarithm, Y, of hydraulic conductivity). We consider (1) the analytical solutions of Riva et al. (Transp Porous Med 45(1):139–193, 2001) for steady-state radial flow in a randomly heterogeneous conductivity field, which we take as references; and (2) the numerical solutions of the MEs satisfied by the (ensemble) mean and (co)variance of hydraulic head and fluxes. Based on 45 numerical grids associated with differing degrees of discretization, we find a supra-linear rate of convergence for the mean and (co)variance of hydraulic head and for the variance of the transverse component of fluxes, the variance of radial fluxes being characterized by a sub-linear convergence rate. Our estimated values of GCI suggest that an accurate computation of mean and (co)variance of head and fluxes requires a space discretization comprising at least 8 grid elements per correlation length of Y, an even finer discretization being required for an accurate representation of the second-order component of mean heads.
12 schema:genre article
13 schema:inLanguage en
14 schema:isAccessibleForFree true
15 schema:isPartOf N56ef5040556a4ed78d5b0d39bba6b04b
16 Naac3714a8cc343a183bfa6785662d788
17 sg:journal.1039987
18 schema:keywords GCI
19 Rivas
20 accurate computation
21 accurate representation
22 al
23 analytical solution
24 assessment
25 components
26 computation
27 conductivity field
28 convergence
29 convergence index
30 convergence rate
31 convergence study
32 correlation length
33 degree
34 degree of discretization
35 discretization
36 elements
37 equations
38 field
39 fine discretization
40 flow
41 flux
42 grid
43 grid convergence
44 grid convergence index
45 grid convergence study
46 grid elements
47 groundwater flow
48 head
49 heterogeneous conductivity fields
50 hydraulic head
51 index
52 length
53 mean head
54 means
55 moment equations
56 numerical grid
57 numerical solution
58 order
59 quantitative assessment
60 radial flow
61 radial flux
62 rate
63 rate/order
64 reference
65 representation
66 results
67 second order
68 second-order components
69 solution
70 space discretization
71 steady-state groundwater flow
72 steady-state radial flow
73 stochastic moment equations
74 study
75 sub-linear convergence rate
76 supra-linear rate
77 terms
78 transverse components
79 values
80 values of GCI
81 variance
82 schema:name Grid convergence for numerical solutions of stochastic moment equations of groundwater flow
83 schema:pagination 1565-1579
84 schema:productId Ne073fd8cd46c4bcd99478bae66a6b494
85 Nf7fd5ccfe07a4a3882e732ad0a1f181c
86 schema:sameAs https://app.dimensions.ai/details/publication/pub.1120876362
87 https://doi.org/10.1007/s00477-019-01719-6
88 schema:sdDatePublished 2022-01-01T18:49
89 schema:sdLicense https://scigraph.springernature.com/explorer/license/
90 schema:sdPublisher Ne9969439bee6462ead87f558344aaf49
91 schema:url https://doi.org/10.1007/s00477-019-01719-6
92 sgo:license sg:explorer/license/
93 sgo:sdDataset articles
94 rdf:type schema:ScholarlyArticle
95 N1a74b31ddfb8486bb8bab384e33e1646 rdf:first sg:person.01337311443.28
96 rdf:rest N4da58efe613447d7943fe20d47fb8461
97 N4da58efe613447d7943fe20d47fb8461 rdf:first sg:person.012556140447.41
98 rdf:rest Nf514b60f2aea4db7b2649153cbd48aa5
99 N56ef5040556a4ed78d5b0d39bba6b04b schema:issueNumber 8-9
100 rdf:type schema:PublicationIssue
101 Naac3714a8cc343a183bfa6785662d788 schema:volumeNumber 33
102 rdf:type schema:PublicationVolume
103 Ncaf9683a280244069f7e0161f9387ff1 rdf:first sg:person.012527715750.15
104 rdf:rest N1a74b31ddfb8486bb8bab384e33e1646
105 Ne073fd8cd46c4bcd99478bae66a6b494 schema:name doi
106 schema:value 10.1007/s00477-019-01719-6
107 rdf:type schema:PropertyValue
108 Ne9969439bee6462ead87f558344aaf49 schema:name Springer Nature - SN SciGraph project
109 rdf:type schema:Organization
110 Nea27f7b164b547ac945690bf5088c0ca rdf:first sg:person.011325456565.14
111 rdf:rest rdf:nil
112 Nf514b60f2aea4db7b2649153cbd48aa5 rdf:first sg:person.013140342153.18
113 rdf:rest Nea27f7b164b547ac945690bf5088c0ca
114 Nf7fd5ccfe07a4a3882e732ad0a1f181c schema:name dimensions_id
115 schema:value pub.1120876362
116 rdf:type schema:PropertyValue
117 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
118 schema:name Mathematical Sciences
119 rdf:type schema:DefinedTerm
120 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
121 schema:name Numerical and Computational Mathematics
122 rdf:type schema:DefinedTerm
123 sg:grant.8231944 http://pending.schema.org/fundedItem sg:pub.10.1007/s00477-019-01719-6
124 rdf:type schema:MonetaryGrant
125 sg:grant.8277564 http://pending.schema.org/fundedItem sg:pub.10.1007/s00477-019-01719-6
126 rdf:type schema:MonetaryGrant
127 sg:journal.1039987 schema:issn 1436-3240
128 1436-3259
129 schema:name Stochastic Environmental Research and Risk Assessment
130 schema:publisher Springer Nature
131 rdf:type schema:Periodical
132 sg:person.011325456565.14 schema:affiliation grid-institutes:grid.11843.3f
133 schema:familyName Ackerer
134 schema:givenName Philippe
135 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011325456565.14
136 rdf:type schema:Person
137 sg:person.012527715750.15 schema:affiliation grid-institutes:grid.258164.c
138 schema:familyName Xia
139 schema:givenName Chuan-An
140 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012527715750.15
141 rdf:type schema:Person
142 sg:person.012556140447.41 schema:affiliation grid-institutes:grid.258164.c
143 schema:familyName Hu
144 schema:givenName Bill X.
145 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012556140447.41
146 rdf:type schema:Person
147 sg:person.013140342153.18 schema:affiliation grid-institutes:grid.134563.6
148 schema:familyName Riva
149 schema:givenName Monica
150 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013140342153.18
151 rdf:type schema:Person
152 sg:person.01337311443.28 schema:affiliation grid-institutes:grid.134563.6
153 schema:familyName Guadagnini
154 schema:givenName Alberto
155 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01337311443.28
156 rdf:type schema:Person
157 sg:pub.10.1007/s00477-003-0154-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048479377
158 https://doi.org/10.1007/s00477-003-0154-4
159 rdf:type schema:CreativeWork
160 sg:pub.10.1007/s00477-003-0161-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030430208
161 https://doi.org/10.1007/s00477-003-0161-5
162 rdf:type schema:CreativeWork
163 sg:pub.10.1007/s00477-005-0023-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043846797
164 https://doi.org/10.1007/s00477-005-0023-4
165 rdf:type schema:CreativeWork
166 sg:pub.10.1023/a:1011880602668 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008657512
167 https://doi.org/10.1023/a:1011880602668
168 rdf:type schema:CreativeWork
169 sg:pub.10.1023/a:1022277418570 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036663944
170 https://doi.org/10.1023/a:1022277418570
171 rdf:type schema:CreativeWork
172 grid-institutes:grid.11843.3f schema:alternateName CNRS, Lab Hydrol & Geochim Strasbourg, Univ Strasbourg, 1 Rue Blessig, 67084, Strasbourg, France
173 schema:name CNRS, Lab Hydrol & Geochim Strasbourg, Univ Strasbourg, 1 Rue Blessig, 67084, Strasbourg, France
174 Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Milan, Italy
175 rdf:type schema:Organization
176 grid-institutes:grid.134563.6 schema:alternateName Department of Hydrology and Atmospheric Sciences, The University of Arizona, Tucson, USA
177 schema:name Department of Hydrology and Atmospheric Sciences, The University of Arizona, Tucson, USA
178 Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Milan, Italy
179 rdf:type schema:Organization
180 grid-institutes:grid.258164.c schema:alternateName Institute of Groundwater and Earth Science, Jinan University, 510632, Guangzhou, China
181 schema:name Institute of Groundwater and Earth Science, Jinan University, 510632, Guangzhou, China
182 rdf:type schema:Organization
 




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


...