ON TWO-SCALE ANALYSIS OF HETEROGENEOUS MATERIALS BY MEANS OF THE MESHLESS FINITE DIFFERENCE METHOD

2016 ◽  
Vol 14 (2) ◽  
pp. 113-134 ◽  
Author(s):  
Irena Jaworska ◽  
Sławomir Milewski
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Heterogeneous Materials ◽  
Scale Analysis ◽  
Meshless Finite Difference Method

A Meshless Finite Difference Method for Conjugate Heat Conduction Problems

2009 ◽  
Author(s):  
Chandrashekhar Varanasi ◽  
Jayathi Y. Murthy ◽  
Sanjay Mathur
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Conjugate Heat Transfer ◽  
Sparse Matrix ◽  
Complex Geometries ◽  
Meshless Finite Difference Method ◽  
Transfer Problems

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.

A Meshless Finite Difference Method for Conjugate Heat Conduction Problems

2010 ◽  
Vol 132 (8) ◽  
Author(s):  
Chandrashekhar Varanasi ◽  
Jayathi Y. Murthy ◽  
Sanjay Mathur
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Conjugate Heat Transfer ◽  
Weighted Least Squares ◽  
Arbitrary Distribution ◽  
Meshless Finite Difference Method ◽  
Transfer Problems

A meshless finite difference method is developed for solving conjugate heat transfer problems. Starting with an arbitrary distribution of mesh points, derivatives are evaluated using a weighted least-squares procedure. The resulting system of algebraic equations is sparse and is solved using an algebraic multigrid method. The implementation of the Neumann, Dirichlet, and mixed boundary conditions within this framework is described. For conjugate heat transfer problems, continuity of the heat flux and temperature are imposed on mesh points at multimaterial interfaces. 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. The method improves on existing meshless methods for conjugate heat conduction by eliminating spurious oscillations previously observed. Metrics for accuracy are provided and future extensions are discussed.

Sign in / Sign up

Export Citation Format

Share Document