Detecting Two-Dimensional Fingering Patterns in a Non-Equilibrium PDE Model via Adaptive Moving Meshes View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2022-08

AUTHORS

P. A. Zegeling

ABSTRACT

This article discusses an adaptive mesh method applied to a bifurcation problem in a non-equilibrium Richard’s equation from hydrology. The extension of this PDE model for the water saturation S, to take into account additional dynamic memory effects gives rise to an extra third-order mixed space-time derivative term in the PDE. The one-space dimensional case predicts the formation of steep non-monotone waves depending on the non-equilibrium parameter. In two space dimensions, this parameter and the frequency in a small perturbation term, predict that the waves may become unstable, thereby initiating so-called gravity-driven fingers. To detect the steep solutions of the time-dependent PDE model, we have used a sophisticated adaptive moving mesh method based on a scaled monitor function. More... »

PAGES

1331-1344

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1134/s0965542522080140

DOI

http://dx.doi.org/10.1134/s0965542522080140

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1150918522


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/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Utrecht University, Utrecht, The Netherlands", 
          "id": "http://www.grid.ac/institutes/grid.5477.1", 
          "name": [
            "Utrecht University, Utrecht, The Netherlands"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Zegeling", 
        "givenName": "P. A.", 
        "id": "sg:person.013632557477.80", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013632557477.80"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/s11242-004-5473-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1029644530", 
          "https://doi.org/10.1007/s11242-004-5473-5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/pl00004242", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1039618757", 
          "https://doi.org/10.1007/pl00004242"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00178771", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1035692482", 
          "https://doi.org/10.1007/bf00178771"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10915-004-4618-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1029337268", 
          "https://doi.org/10.1007/s10915-004-4618-6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s002110050182", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003874423", 
          "https://doi.org/10.1007/s002110050182"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2022-08", 
    "datePublishedReg": "2022-08-01", 
    "description": "This article discusses an adaptive mesh method applied to a bifurcation problem in a non-equilibrium Richard\u2019s equation from hydrology. The extension of this PDE model for the water saturation S, to take into account additional dynamic memory effects gives rise to an extra third-order mixed space-time derivative term in the PDE. The one-space dimensional case predicts the formation of steep non-monotone waves depending on the non-equilibrium parameter. In two space dimensions, this parameter and the frequency in a small perturbation term, predict that the waves may become unstable, thereby initiating so-called gravity-driven fingers. To detect the steep solutions of the time-dependent PDE model, we have used a sophisticated adaptive moving mesh method based on a scaled monitor function.", 
    "genre": "article", 
    "id": "sg:pub.10.1134/s0965542522080140", 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136025", 
        "issn": [
          "0965-5425", 
          "1555-6662"
        ], 
        "name": "Computational Mathematics and Mathematical Physics", 
        "publisher": "Pleiades Publishing", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "8", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "62"
      }
    ], 
    "keywords": [
      "PDE model", 
      "Non-Equilibrium Richards Equation", 
      "non-monotone waves", 
      "mesh method", 
      "adaptive mesh method", 
      "derivative terms", 
      "space dimensions", 
      "bifurcation problem", 
      "small perturbation term", 
      "gravity\u2010driven fingers", 
      "dimensional case", 
      "perturbation terms", 
      "Moving Mesh", 
      "dynamic memory effects", 
      "monitor function", 
      "Richards equation", 
      "non-equilibrium parameter", 
      "steep solutions", 
      "equations", 
      "fingering patterns", 
      "waves", 
      "PDEs", 
      "saturation S", 
      "memory effect", 
      "model", 
      "parameters", 
      "mesh", 
      "terms", 
      "adaptive", 
      "problem", 
      "solution", 
      "extension", 
      "dimensions", 
      "function", 
      "method", 
      "hydrology", 
      "cases", 
      "frequency", 
      "formation", 
      "effect", 
      "article", 
      "finger", 
      "patterns"
    ], 
    "name": "Detecting Two-Dimensional Fingering Patterns in a Non-Equilibrium PDE Model via Adaptive Moving Meshes", 
    "pagination": "1331-1344", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1150918522"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1134/s0965542522080140"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1134/s0965542522080140", 
      "https://app.dimensions.ai/details/publication/pub.1150918522"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-11-24T21:08", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20221124/entities/gbq_results/article/article_943.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1134/s0965542522080140"
  }
]
 

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.10.1134/s0965542522080140'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1134/s0965542522080140'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1134/s0965542522080140'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1134/s0965542522080140'


 

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

120 TRIPLES      21 PREDICATES      72 URIs      59 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1134/s0965542522080140 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N2f6dcc4244f24741b24847c2b7266fd9
4 schema:citation sg:pub.10.1007/bf00178771
5 sg:pub.10.1007/pl00004242
6 sg:pub.10.1007/s002110050182
7 sg:pub.10.1007/s10915-004-4618-6
8 sg:pub.10.1007/s11242-004-5473-5
9 schema:datePublished 2022-08
10 schema:datePublishedReg 2022-08-01
11 schema:description This article discusses an adaptive mesh method applied to a bifurcation problem in a non-equilibrium Richard’s equation from hydrology. The extension of this PDE model for the water saturation S, to take into account additional dynamic memory effects gives rise to an extra third-order mixed space-time derivative term in the PDE. The one-space dimensional case predicts the formation of steep non-monotone waves depending on the non-equilibrium parameter. In two space dimensions, this parameter and the frequency in a small perturbation term, predict that the waves may become unstable, thereby initiating so-called gravity-driven fingers. To detect the steep solutions of the time-dependent PDE model, we have used a sophisticated adaptive moving mesh method based on a scaled monitor function.
12 schema:genre article
13 schema:isAccessibleForFree false
14 schema:isPartOf N1d534314f66b49caba17e6099509120b
15 N69c6ecbd14bf4f33a36554e9a9b0ec2a
16 sg:journal.1136025
17 schema:keywords Moving Mesh
18 Non-Equilibrium Richards Equation
19 PDE model
20 PDEs
21 Richards equation
22 adaptive
23 adaptive mesh method
24 article
25 bifurcation problem
26 cases
27 derivative terms
28 dimensional case
29 dimensions
30 dynamic memory effects
31 effect
32 equations
33 extension
34 finger
35 fingering patterns
36 formation
37 frequency
38 function
39 gravity‐driven fingers
40 hydrology
41 memory effect
42 mesh
43 mesh method
44 method
45 model
46 monitor function
47 non-equilibrium parameter
48 non-monotone waves
49 parameters
50 patterns
51 perturbation terms
52 problem
53 saturation S
54 small perturbation term
55 solution
56 space dimensions
57 steep solutions
58 terms
59 waves
60 schema:name Detecting Two-Dimensional Fingering Patterns in a Non-Equilibrium PDE Model via Adaptive Moving Meshes
61 schema:pagination 1331-1344
62 schema:productId Ncc92898608f742d28171b80399e8a26f
63 Nfe8a89d5724c4533be3276115f96b15c
64 schema:sameAs https://app.dimensions.ai/details/publication/pub.1150918522
65 https://doi.org/10.1134/s0965542522080140
66 schema:sdDatePublished 2022-11-24T21:08
67 schema:sdLicense https://scigraph.springernature.com/explorer/license/
68 schema:sdPublisher N38a0b499e24143efa7bdb57c264687d7
69 schema:url https://doi.org/10.1134/s0965542522080140
70 sgo:license sg:explorer/license/
71 sgo:sdDataset articles
72 rdf:type schema:ScholarlyArticle
73 N1d534314f66b49caba17e6099509120b schema:issueNumber 8
74 rdf:type schema:PublicationIssue
75 N2f6dcc4244f24741b24847c2b7266fd9 rdf:first sg:person.013632557477.80
76 rdf:rest rdf:nil
77 N38a0b499e24143efa7bdb57c264687d7 schema:name Springer Nature - SN SciGraph project
78 rdf:type schema:Organization
79 N69c6ecbd14bf4f33a36554e9a9b0ec2a schema:volumeNumber 62
80 rdf:type schema:PublicationVolume
81 Ncc92898608f742d28171b80399e8a26f schema:name doi
82 schema:value 10.1134/s0965542522080140
83 rdf:type schema:PropertyValue
84 Nfe8a89d5724c4533be3276115f96b15c schema:name dimensions_id
85 schema:value pub.1150918522
86 rdf:type schema:PropertyValue
87 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
88 schema:name Mathematical Sciences
89 rdf:type schema:DefinedTerm
90 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
91 schema:name Pure Mathematics
92 rdf:type schema:DefinedTerm
93 sg:journal.1136025 schema:issn 0965-5425
94 1555-6662
95 schema:name Computational Mathematics and Mathematical Physics
96 schema:publisher Pleiades Publishing
97 rdf:type schema:Periodical
98 sg:person.013632557477.80 schema:affiliation grid-institutes:grid.5477.1
99 schema:familyName Zegeling
100 schema:givenName P. A.
101 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013632557477.80
102 rdf:type schema:Person
103 sg:pub.10.1007/bf00178771 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035692482
104 https://doi.org/10.1007/bf00178771
105 rdf:type schema:CreativeWork
106 sg:pub.10.1007/pl00004242 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039618757
107 https://doi.org/10.1007/pl00004242
108 rdf:type schema:CreativeWork
109 sg:pub.10.1007/s002110050182 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003874423
110 https://doi.org/10.1007/s002110050182
111 rdf:type schema:CreativeWork
112 sg:pub.10.1007/s10915-004-4618-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029337268
113 https://doi.org/10.1007/s10915-004-4618-6
114 rdf:type schema:CreativeWork
115 sg:pub.10.1007/s11242-004-5473-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029644530
116 https://doi.org/10.1007/s11242-004-5473-5
117 rdf:type schema:CreativeWork
118 grid-institutes:grid.5477.1 schema:alternateName Utrecht University, Utrecht, The Netherlands
119 schema:name Utrecht University, Utrecht, The Netherlands
120 rdf:type schema:Organization
 




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


...