In recent years, there has been a great deal of interest in developing meshless methods for computational fluid dynamics (CFD) applications. In this paper, a meshless finite difference method is developed for solving conjugate heat transfer problems in complex geometries. Traditional finite difference methods (FDMs) have been restricted to an orthogonal or a body-fitted distribution of points. However, the Taylor series upon which the FDM is based is valid at any location in the neighborhood of the point about which the expansion is carried out. Exploiting this fact, and starting with an unstructured distribution of mesh points, derivatives are evaluated using a weighted least squares procedure. The system of equations that results from this discretization can be represented by a sparse matrix. This system is solved with an algebraic multigrid (AMG) solver. The implementation of Neumann, Dirichlet and mixed boundary conditions within this framework is described, as well as the handling of conjugate heat transfer. The method is verified through application to classical heat conduction problems with known analytical solutions. It is then applied to the solution of conjugate heat transfer problems in complex geometries, and the solutions so obtained are compared with more conventional unstructured finite volume methods. Metrics for accuracy are provided and future extensions are discussed.
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ASME 2009 Heat Transfer Summer Conference collocated with the InterPACK09 and 3rd Energy Sustainability Conferences
July 19–23, 2009
San Francisco, California, USA
Conference Sponsors:
- Heat Transfer Division
ISBN:
978-0-7918-4357-4
PROCEEDINGS PAPER
A Meshless Finite Difference Method for Conjugate Heat Conduction Problems
Chandrashekhar Varanasi,
Chandrashekhar Varanasi
Purdue University, West Lafayette, IN
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Jayathi Y. Murthy,
Jayathi Y. Murthy
Purdue University, West Lafayette, IN
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Sanjay Mathur
Sanjay Mathur
Purdue University, West Lafayette, IN
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Chandrashekhar Varanasi
Purdue University, West Lafayette, IN
Jayathi Y. Murthy
Purdue University, West Lafayette, IN
Sanjay Mathur
Purdue University, West Lafayette, IN
Paper No:
HT2009-88098, pp. 633-644; 12 pages
Published Online:
March 12, 2010
Citation
Varanasi, C, Murthy, JY, & Mathur, S. "A Meshless Finite Difference Method for Conjugate Heat Conduction Problems." Proceedings of the ASME 2009 Heat Transfer Summer Conference collocated with the InterPACK09 and 3rd Energy Sustainability Conferences. Volume 2: Theory and Fundamental Research; Aerospace Heat Transfer; Gas Turbine Heat Transfer; Computational Heat Transfer. San Francisco, California, USA. July 19–23, 2009. pp. 633-644. ASME. https://doi.org/10.1115/HT2009-88098
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