Solution structures for imposing boundary conditions in mesh free analysis of heat conduction problems

Linxia Gu, Ashok V. Kumar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

One of the main advantages of meshless methods is that it eliminates the mesh generation, but it is still necessary to place nodes with controlled spacing variation on the boundary and within the domain. However, due to lack of connectivity between nodes it is more difficult to interpolate the field variables and impose boundary conditions. In this paper, a mesh free method is presented for analysis using a structured grid that does not conform to the geometry of the domain. The geometry of the domain is independent of the structured grid and is represented using implicit equations. The implicit equations of the boundaries can be used to construct solution structures that satisfy boundary conditions exactly even though the nodes of the grid are not on the boundaries of the domain. The solution structures are constructed using the implicit equations of the boundary together with a piece-wise interpolation over the structured grid. The implicit equations are also used to construct step function of solid such that its value is equal to unity inside the solid and zero outside. The step function of the solid is used for volume integrations needed for the analysis. The traditional weak form for Poisson's equation is modified by using this solution structure to eliminate the surface integration terms. The accuracy and implementation of the present mesh free method is illustrated for two-dimensional heat conduction problems governed by Poisson's equation. Satisfactory results are obtained when compared with analytical results and results from commercial finite element software.

Original languageEnglish (US)
Title of host publicationProceedings of the ASME Heat Transfer Division 2005
Pages157-165
Number of pages9
Edition1
DOIs
StatePublished - Dec 1 2005
Event2005 ASME International Mechanical Engineering Congress and Exposition, IMECE 2005 - Orlando, FL, United States
Duration: Nov 5 2005Nov 11 2005

Publication series

NameAmerican Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD
Number1
Volume376 HTD
ISSN (Print)0272-5673

Conference

Conference2005 ASME International Mechanical Engineering Congress and Exposition, IMECE 2005
CountryUnited States
CityOrlando, FL
Period11/5/0511/11/05

Fingerprint

Heat conduction
Poisson equation
Boundary conditions
Mesh generation
Geometry
Interpolation

Keywords

  • Boolean operation
  • Implicit solid element
  • Meshfree method
  • Solution structure
  • Step function
  • Uniform grid

ASJC Scopus subject areas

  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

Cite this

Gu, L., & Kumar, A. V. (2005). Solution structures for imposing boundary conditions in mesh free analysis of heat conduction problems. In Proceedings of the ASME Heat Transfer Division 2005 (1 ed., pp. 157-165). (American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD; Vol. 376 HTD, No. 1). https://doi.org/10.1115/IMECE2005-80872

Solution structures for imposing boundary conditions in mesh free analysis of heat conduction problems. / Gu, Linxia; Kumar, Ashok V.

Proceedings of the ASME Heat Transfer Division 2005. 1. ed. 2005. p. 157-165 (American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD; Vol. 376 HTD, No. 1).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Gu, L & Kumar, AV 2005, Solution structures for imposing boundary conditions in mesh free analysis of heat conduction problems. in Proceedings of the ASME Heat Transfer Division 2005. 1 edn, American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD, no. 1, vol. 376 HTD, pp. 157-165, 2005 ASME International Mechanical Engineering Congress and Exposition, IMECE 2005, Orlando, FL, United States, 11/5/05. https://doi.org/10.1115/IMECE2005-80872
Gu L, Kumar AV. Solution structures for imposing boundary conditions in mesh free analysis of heat conduction problems. In Proceedings of the ASME Heat Transfer Division 2005. 1 ed. 2005. p. 157-165. (American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD; 1). https://doi.org/10.1115/IMECE2005-80872
Gu, Linxia ; Kumar, Ashok V. / Solution structures for imposing boundary conditions in mesh free analysis of heat conduction problems. Proceedings of the ASME Heat Transfer Division 2005. 1. ed. 2005. pp. 157-165 (American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD; 1).
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