WEKO3
AND
Item
{"_buckets": {"deposit": "cc0673d9ff5242d6a61a3972fd5494b9"}, "_deposit": {"id": "8800", "owners": [], "pid": {"revision_id": 0, "type": "depid", "value": "8800"}, "status": "published"}, "_oai": {"id": "oai:tsukuba.repo.nii.ac.jp:00008800"}, "item_12_biblio_info_6": {"attribute_name": "\u66f8\u8a8c\u60c5\u5831", "attribute_value_mlt": [{"bibliographicIssueDates": {"bibliographicIssueDate": "1994", "bibliographicIssueDateType": "Issued"}, "bibliographic_titles": [{}]}]}, "item_12_creator_3": {"attribute_name": "\u8457\u8005\u5225\u540d", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "\u5468, \u5049\u6771"}], "nameIdentifiers": [{"nameIdentifier": "35968", "nameIdentifierScheme": "WEKO"}]}]}, "item_12_description_14": {"attribute_name": "\u30d5\u30a9\u30fc\u30de\u30c3\u30c8", "attribute_value_mlt": [{"subitem_description": "application/pdf", "subitem_description_type": "Other"}]}, "item_12_description_33": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "attribute_value_mlt": [{"subitem_description": "text", "subitem_description_type": "Other"}]}, "item_12_description_4": {"attribute_name": "\u6284\u9332", "attribute_value_mlt": [{"subitem_description": "A free surface B\u00e9nard problem, in which a horizontal layer of fluid with a deformable free surface is considered to be situated on a hot rigid plate, is proposed to study equilibrium instability and convective bifurcation phenomena of natural convection heated from below with a free surface. This problem is formulated as a free boundary problem governed by Boussinesq equations. A numerical approach using a spectral method is proposed to solve the free boundary problems. To cope with unknown and moving boundary, fixed domain method is applied to transform free boundary domain into fixed boundary domain in which the collocation spectral method is used. Numerical results of several test problems indicatid that the free boundary problem calculated by spectral method is of much better precision than calculated by finite defference method. A FourierChebyshev collocation spectral method is presented for numerical calculation of the free surface B\u00e9nard problem. The twodimensional periodic Boussinesq equations are directly simulated for numerical analysis of equilibrium instability and convective bifurcation phenomena in the free surface B\u00e9nard problem of a specific fluid in a specific geometric region. In comparison with the free surface B\u00e9rnard problem, the rigid surface B\u00e9nard problem, a typical B\u00e9rnard problem in which a horizontal fluid bounded by two rigid plates is considered to be heated from below, is calculated as well. Numerical results have revealed that in the free surface B\u00e9nard problem, there exists also a stationary(steady) bifurcation solution of convection rolls which are wellknown in the rigid surface B\u00e9nard probelm. The convection rolls are symmetry and sruface is flat in the rigid surface B\u00e9nard Problem, whereas the convection rolls are asymmetry and surface is significantly curved in the free surface B\u00e9nard problem to show the effect of a deformable free surface and its surface tension. Moreover, the numerical experiments indicate that there also exits a critical Rayleigh number in the free surface B\u00e9nard probelm; when the Rayleigh number is smaller than the critical Rayleigh number, there is only a static solution; when the Rayleigh number is larger than the critical Rayleigh number, there occurs a bifurcation of convection rolls. The critical Rayleigh number has been investigated by numerical experiments and results show that the value of the critical Rayleigh number for the free surface B\u00e9nard problem is smaller than that for the rigid surface B\u00e9nard probelm.This indicates that equilibrium is less stable when there is a free surface and that it is easier for the onset of convection rolls in the free surface B\u00e9nard problem than in the rigid surface B\u00e9nard problem. Furthermore, the free surface B\u00e9nard problem is studied by a linear stability theory to support the results indecated by direct simulations. The linearized perturbance boundary value problem is derived. The eigenvalues are numerically calculated to investigate the critical Rayleigh number. The critical Rayleigh number in vestigated by the linear stability theory shows satisfactory agreement with the critical Rayleigh number investigated by direct numerical simulations.", "subitem_description_type": "Abstract"}]}, "item_12_description_5": {"attribute_name": "\u5185\u5bb9\u8a18\u8ff0", "attribute_value_mlt": [{"subitem_description": "Thesis (Ph.D. in Engineering)University of Tsukuba, (A), no. 1255, 1994.3.25", "subitem_description_type": "Other"}]}, "item_12_identifier_34": {"attribute_name": "URI", "attribute_value_mlt": [{"subitem_identifier_type": "HDL", "subitem_identifier_uri": "http://hdl.handle.net/2241/6465"}]}, "item_12_select_15": {"attribute_name": "\u8457\u8005\u7248\u30d5\u30e9\u30b0", "attribute_value_mlt": [{"subitem_select_item": "author"}]}, "item_12_subject_16": {"attribute_name": "\u65e5\u672c\u5341\u9032\u5206\u985e\u6cd5", "attribute_value_mlt": [{"subitem_subject": "423.8", "subitem_subject_scheme": "NDC"}]}, "item_12_subject_20": {"attribute_name": "NII\u30b5\u30d6\u30b8\u30a7\u30af\u30c8", "attribute_value_mlt": [{"subitem_subject": "\u7269\u7406\u5b66", "subitem_subject_scheme": "Other"}]}, "item_creator": {"attribute_name": "\u8457\u8005", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "Zhou, Weidong"}], "nameIdentifiers": [{"nameIdentifier": "35967", "nameIdentifierScheme": "WEKO"}]}]}, "item_files": {"attribute_name": "\u30d5\u30a1\u30a4\u30eb\u60c5\u5831", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "20131218"}], "displaytype": "detail", "download_preview_message": "", "file_order": 0, "filename": "A1255.pdf", "filesize": [{"value": "93.8 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_free", "mimetype": "application/pdf", "size": 93800.0, "url": {"label": "A1255.pdf", "url": "https://tsukuba.repo.nii.ac.jp/record/8800/files/A1255.pdf"}, "version_id": "f9a34664dc2f4272b9e609bf8d2fd6f2"}]}, "item_language": {"attribute_name": "\u8a00\u8a9e", "attribute_value_mlt": [{"subitem_language": "jpn"}]}, "item_resource_type": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "attribute_value_mlt": [{"resourcetype": "thesis", "resourceuri": "http://purl.org/coar/resource_type/c_46ec"}]}, "item_title": "Numerical analysis of natural convection with a free surface using a spectral method", "item_titles": {"attribute_name": "\u30bf\u30a4\u30c8\u30eb", "attribute_value_mlt": [{"subitem_title": "Numerical analysis of natural convection with a free surface using a spectral method"}]}, "item_type_id": "12", "owner": "1", "path": ["3/233/244"], "permalink_uri": "http://hdl.handle.net/2241/6465", "pubdate": {"attribute_name": "\u516c\u958b\u65e5", "attribute_name_i18n": "\u516c\u958b\u65e5", "attribute_value": "20070725"}, "publish_date": "20070725", "publish_status": "0", "recid": "8800", "relation": {}, "relation_version_is_last": true, "title": ["Numerical analysis of natural convection with a free surface using a spectral method"], "weko_shared_id": null}
Numerical analysis of natural convection with a free surface using a spectral method
http://hdl.handle.net/2241/6465
6106eeb132794e70b157976a9fea9b69
Name / File  License  Actions  

A1255.pdf (93.8 kB)


item type  Thesis or Dissertation(1)  

公開日  20070725  
タイトル  
タイトル  Numerical analysis of natural convection with a free surface using a spectral method  
言語  
言語  jpn  
資源タイプ  
資源  http://purl.org/coar/resource_type/c_46ec  
タイプ  thesis  
著者 
Zhou, Weidong
× Zhou, Weidong 

著者別名 
周, 偉東
× 周, 偉東 

抄録  
内容記述  A free surface Bénard problem, in which a horizontal layer of fluid with a deformable free surface is considered to be situated on a hot rigid plate, is proposed to study equilibrium instability and convective bifurcation phenomena of natural convection heated from below with a free surface. This problem is formulated as a free boundary problem governed by Boussinesq equations. A numerical approach using a spectral method is proposed to solve the free boundary problems. To cope with unknown and moving boundary, fixed domain method is applied to transform free boundary domain into fixed boundary domain in which the collocation spectral method is used. Numerical results of several test problems indicatid that the free boundary problem calculated by spectral method is of much better precision than calculated by finite defference method. A FourierChebyshev collocation spectral method is presented for numerical calculation of the free surface Bénard problem. The twodimensional periodic Boussinesq equations are directly simulated for numerical analysis of equilibrium instability and convective bifurcation phenomena in the free surface Bénard problem of a specific fluid in a specific geometric region. In comparison with the free surface Bérnard problem, the rigid surface Bénard problem, a typical Bérnard problem in which a horizontal fluid bounded by two rigid plates is considered to be heated from below, is calculated as well. Numerical results have revealed that in the free surface Bénard problem, there exists also a stationary(steady) bifurcation solution of convection rolls which are wellknown in the rigid surface Bénard probelm. The convection rolls are symmetry and sruface is flat in the rigid surface Bénard Problem, whereas the convection rolls are asymmetry and surface is significantly curved in the free surface Bénard problem to show the effect of a deformable free surface and its surface tension. Moreover, the numerical experiments indicate that there also exits a critical Rayleigh number in the free surface Bénard probelm; when the Rayleigh number is smaller than the critical Rayleigh number, there is only a static solution; when the Rayleigh number is larger than the critical Rayleigh number, there occurs a bifurcation of convection rolls. The critical Rayleigh number has been investigated by numerical experiments and results show that the value of the critical Rayleigh number for the free surface Bénard problem is smaller than that for the rigid surface Bénard probelm.This indicates that equilibrium is less stable when there is a free surface and that it is easier for the onset of convection rolls in the free surface Bénard problem than in the rigid surface Bénard problem. Furthermore, the free surface Bénard problem is studied by a linear stability theory to support the results indecated by direct simulations. The linearized perturbance boundary value problem is derived. The eigenvalues are numerically calculated to investigate the critical Rayleigh number. The critical Rayleigh number in vestigated by the linear stability theory shows satisfactory agreement with the critical Rayleigh number investigated by direct numerical simulations.  
内容記述  
内容記述  Thesis (Ph.D. in Engineering)University of Tsukuba, (A), no. 1255, 1994.3.25  
書誌情報  発行日 1994  
著者版フラグ  
値  author  
資源タイプ  
内容記述  text  
URI  
識別子  http://hdl.handle.net/2241/6465  
識別子タイプ  HDL 