Numerical analysis of uncertain temperature field by stochastic finite difference method View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2014-04

AUTHORS

Chong Wang, ZhiPing Qiu, Di Wu

ABSTRACT

Based on the combination of stochastic mathematics and conventional finite difference method, a new numerical computing technique named stochastic finite difference for solving heat conduction problems with random physical parameters, initial and boundary conditions is discussed. Begin with the analysis of steady-state heat conduction problems, difference discrete equations with random parameters are established, and then the computing formulas for the mean value and variance of temperature field are derived by the second-order stochastic parameter perturbation method. Subsequently, the proposed random model and method are extended to the field of transient heat conduction and the new analysis theory of stability applicable to stochastic difference schemes is developed. The layer-by-layer recursive equations for the first two probabilistic moments of the transient temperature field at different time points are quickly obtained and easily solved by programming. Finally, by comparing the results with traditional Monte Carlo simulation, two numerical examples are given to demonstrate the feasibility and effectiveness of the presented method for solving both steady-state and transient heat conduction problems. More... »

PAGES

698-707

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11433-013-5235-x

DOI

http://dx.doi.org/10.1007/s11433-013-5235-x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1030334588


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": "Beihang University", 
          "id": "https://www.grid.ac/institutes/grid.64939.31", 
          "name": [
            "School of Aeronautic Science and Engineering, Beihang University, 100191, Beijing, China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Wang", 
        "givenName": "Chong", 
        "id": "sg:person.012145241544.37", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012145241544.37"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Beihang University", 
          "id": "https://www.grid.ac/institutes/grid.64939.31", 
          "name": [
            "School of Aeronautic Science and Engineering, Beihang University, 100191, Beijing, China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Qiu", 
        "givenName": "ZhiPing", 
        "id": "sg:person.014412456557.05", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014412456557.05"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "China Academy of Launch Vehicle Technology", 
          "id": "https://www.grid.ac/institutes/grid.482529.0", 
          "name": [
            "China Academy of Launch Vehicle Technology, 100076, Beijing, China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Wu", 
        "givenName": "Di", 
        "id": "sg:person.010323611616.22", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010323611616.22"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://app.dimensions.ai/details/publication/pub.1002556993", 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-94-017-1703-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002556993", 
          "https://doi.org/10.1007/978-94-017-1703-8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-94-017-1703-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002556993", 
          "https://doi.org/10.1007/978-94-017-1703-8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0017-9310(03)00299-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006120921"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0017-9310(03)00299-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006120921"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.engfracmech.2006.04.010", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1009789533"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.ijthermalsci.2006.03.001", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1012291923"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0955-7997(03)00058-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1023276871"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0955-7997(03)00058-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1023276871"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0045-7949(95)00267-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1023904569"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0735-1933(99)00068-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025324624"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://app.dimensions.ai/details/publication/pub.1033094591", 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4612-3094-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1033094591", 
          "https://doi.org/10.1007/978-1-4612-3094-6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4612-3094-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1033094591", 
          "https://doi.org/10.1007/978-1-4612-3094-6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0045-7949(98)00058-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1034831098"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0045-7825(96)01168-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1035058244"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2014-04", 
    "datePublishedReg": "2014-04-01", 
    "description": "Based on the combination of stochastic mathematics and conventional finite difference method, a new numerical computing technique named stochastic finite difference for solving heat conduction problems with random physical parameters, initial and boundary conditions is discussed. Begin with the analysis of steady-state heat conduction problems, difference discrete equations with random parameters are established, and then the computing formulas for the mean value and variance of temperature field are derived by the second-order stochastic parameter perturbation method. Subsequently, the proposed random model and method are extended to the field of transient heat conduction and the new analysis theory of stability applicable to stochastic difference schemes is developed. The layer-by-layer recursive equations for the first two probabilistic moments of the transient temperature field at different time points are quickly obtained and easily solved by programming. Finally, by comparing the results with traditional Monte Carlo simulation, two numerical examples are given to demonstrate the feasibility and effectiveness of the presented method for solving both steady-state and transient heat conduction problems.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s11433-013-5235-x", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1282972", 
        "issn": [
          "1674-7348", 
          "1869-1927"
        ], 
        "name": "Science China Physics, Mechanics & Astronomy", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "4", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "57"
      }
    ], 
    "name": "Numerical analysis of uncertain temperature field by stochastic finite difference method", 
    "pagination": "698-707", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "9081f05a7138949096fd581e7df038175133dc87c2c67f9ada1c49594db309ba"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s11433-013-5235-x"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1030334588"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s11433-013-5235-x", 
      "https://app.dimensions.ai/details/publication/pub.1030334588"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-10T20:49", 
    "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_8684_00000522.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2Fs11433-013-5235-x"
  }
]
 

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/s11433-013-5235-x'

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/s11433-013-5235-x'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s11433-013-5235-x'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s11433-013-5235-x'


 

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

114 TRIPLES      21 PREDICATES      39 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s11433-013-5235-x schema:about anzsrc-for:01
2 anzsrc-for:0103
3 schema:author N7a4f545070bc44e4ad617a803f6dfc43
4 schema:citation sg:pub.10.1007/978-1-4612-3094-6
5 sg:pub.10.1007/978-94-017-1703-8
6 https://app.dimensions.ai/details/publication/pub.1002556993
7 https://app.dimensions.ai/details/publication/pub.1033094591
8 https://doi.org/10.1016/0045-7949(95)00267-7
9 https://doi.org/10.1016/j.engfracmech.2006.04.010
10 https://doi.org/10.1016/j.ijthermalsci.2006.03.001
11 https://doi.org/10.1016/s0017-9310(03)00299-0
12 https://doi.org/10.1016/s0045-7825(96)01168-1
13 https://doi.org/10.1016/s0045-7949(98)00058-3
14 https://doi.org/10.1016/s0735-1933(99)00068-8
15 https://doi.org/10.1016/s0955-7997(03)00058-4
16 schema:datePublished 2014-04
17 schema:datePublishedReg 2014-04-01
18 schema:description Based on the combination of stochastic mathematics and conventional finite difference method, a new numerical computing technique named stochastic finite difference for solving heat conduction problems with random physical parameters, initial and boundary conditions is discussed. Begin with the analysis of steady-state heat conduction problems, difference discrete equations with random parameters are established, and then the computing formulas for the mean value and variance of temperature field are derived by the second-order stochastic parameter perturbation method. Subsequently, the proposed random model and method are extended to the field of transient heat conduction and the new analysis theory of stability applicable to stochastic difference schemes is developed. The layer-by-layer recursive equations for the first two probabilistic moments of the transient temperature field at different time points are quickly obtained and easily solved by programming. Finally, by comparing the results with traditional Monte Carlo simulation, two numerical examples are given to demonstrate the feasibility and effectiveness of the presented method for solving both steady-state and transient heat conduction problems.
19 schema:genre research_article
20 schema:inLanguage en
21 schema:isAccessibleForFree false
22 schema:isPartOf N61620edec96140a5b35a5d4ec2820064
23 Nd40eb297602b45769a2957bd5f77ba9d
24 sg:journal.1282972
25 schema:name Numerical analysis of uncertain temperature field by stochastic finite difference method
26 schema:pagination 698-707
27 schema:productId N450dd4db5c71446fb116a034ee6930e8
28 N452f8f6799e3458d99cd30ca652e964e
29 Nbea0eb9051a14eb2857e05c5072c4cad
30 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030334588
31 https://doi.org/10.1007/s11433-013-5235-x
32 schema:sdDatePublished 2019-04-10T20:49
33 schema:sdLicense https://scigraph.springernature.com/explorer/license/
34 schema:sdPublisher N94c0c6fc04474c8d8c994153515a1954
35 schema:url http://link.springer.com/10.1007%2Fs11433-013-5235-x
36 sgo:license sg:explorer/license/
37 sgo:sdDataset articles
38 rdf:type schema:ScholarlyArticle
39 N450dd4db5c71446fb116a034ee6930e8 schema:name dimensions_id
40 schema:value pub.1030334588
41 rdf:type schema:PropertyValue
42 N452f8f6799e3458d99cd30ca652e964e schema:name doi
43 schema:value 10.1007/s11433-013-5235-x
44 rdf:type schema:PropertyValue
45 N61620edec96140a5b35a5d4ec2820064 schema:issueNumber 4
46 rdf:type schema:PublicationIssue
47 N7a4f545070bc44e4ad617a803f6dfc43 rdf:first sg:person.012145241544.37
48 rdf:rest N7ac6b0472f494c62b7827892ebcebfb9
49 N7ac6b0472f494c62b7827892ebcebfb9 rdf:first sg:person.014412456557.05
50 rdf:rest Nf88439ba35944a23989a0b0db22853c6
51 N94c0c6fc04474c8d8c994153515a1954 schema:name Springer Nature - SN SciGraph project
52 rdf:type schema:Organization
53 Nbea0eb9051a14eb2857e05c5072c4cad schema:name readcube_id
54 schema:value 9081f05a7138949096fd581e7df038175133dc87c2c67f9ada1c49594db309ba
55 rdf:type schema:PropertyValue
56 Nd40eb297602b45769a2957bd5f77ba9d schema:volumeNumber 57
57 rdf:type schema:PublicationVolume
58 Nf88439ba35944a23989a0b0db22853c6 rdf:first sg:person.010323611616.22
59 rdf:rest rdf:nil
60 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
61 schema:name Mathematical Sciences
62 rdf:type schema:DefinedTerm
63 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
64 schema:name Numerical and Computational Mathematics
65 rdf:type schema:DefinedTerm
66 sg:journal.1282972 schema:issn 1674-7348
67 1869-1927
68 schema:name Science China Physics, Mechanics & Astronomy
69 rdf:type schema:Periodical
70 sg:person.010323611616.22 schema:affiliation https://www.grid.ac/institutes/grid.482529.0
71 schema:familyName Wu
72 schema:givenName Di
73 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010323611616.22
74 rdf:type schema:Person
75 sg:person.012145241544.37 schema:affiliation https://www.grid.ac/institutes/grid.64939.31
76 schema:familyName Wang
77 schema:givenName Chong
78 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012145241544.37
79 rdf:type schema:Person
80 sg:person.014412456557.05 schema:affiliation https://www.grid.ac/institutes/grid.64939.31
81 schema:familyName Qiu
82 schema:givenName ZhiPing
83 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014412456557.05
84 rdf:type schema:Person
85 sg:pub.10.1007/978-1-4612-3094-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033094591
86 https://doi.org/10.1007/978-1-4612-3094-6
87 rdf:type schema:CreativeWork
88 sg:pub.10.1007/978-94-017-1703-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002556993
89 https://doi.org/10.1007/978-94-017-1703-8
90 rdf:type schema:CreativeWork
91 https://app.dimensions.ai/details/publication/pub.1002556993 schema:CreativeWork
92 https://app.dimensions.ai/details/publication/pub.1033094591 schema:CreativeWork
93 https://doi.org/10.1016/0045-7949(95)00267-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023904569
94 rdf:type schema:CreativeWork
95 https://doi.org/10.1016/j.engfracmech.2006.04.010 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009789533
96 rdf:type schema:CreativeWork
97 https://doi.org/10.1016/j.ijthermalsci.2006.03.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012291923
98 rdf:type schema:CreativeWork
99 https://doi.org/10.1016/s0017-9310(03)00299-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006120921
100 rdf:type schema:CreativeWork
101 https://doi.org/10.1016/s0045-7825(96)01168-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035058244
102 rdf:type schema:CreativeWork
103 https://doi.org/10.1016/s0045-7949(98)00058-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034831098
104 rdf:type schema:CreativeWork
105 https://doi.org/10.1016/s0735-1933(99)00068-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025324624
106 rdf:type schema:CreativeWork
107 https://doi.org/10.1016/s0955-7997(03)00058-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023276871
108 rdf:type schema:CreativeWork
109 https://www.grid.ac/institutes/grid.482529.0 schema:alternateName China Academy of Launch Vehicle Technology
110 schema:name China Academy of Launch Vehicle Technology, 100076, Beijing, China
111 rdf:type schema:Organization
112 https://www.grid.ac/institutes/grid.64939.31 schema:alternateName Beihang University
113 schema:name School of Aeronautic Science and Engineering, Beihang University, 100191, Beijing, China
114 rdf:type schema:Organization
 




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


...