Heat Diffusion in Heterogeneous Bodies Using Heat-Flux-Conserving Basis Functions

1988 ◽  
Vol 110 (2) ◽  
pp. 276-282 ◽  
Author(s):  
A. Haji-Sheikh
Keyword(s):  
Heat Flux ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Difference Method ◽  
Solution Method ◽  
Basis Functions ◽  
Heat Diffusion ◽  
Simple Geometry ◽  
The Finite Difference Method

The generalized analytical derivation presented here enables one to obtain solutions to the diffusion equation in complex heterogeneous geometries. A new method of constructing basis functions is introduced that preserves the continuity of temperature and heat flux throughout the domain, specifically at the boundary of each inclusion. A set of basis functions produced in this manner can be used in conjunction with the Green’s function derived through the Galerkin procedure to produce a useful solution method. A simple geometry is selected for comparison with the finite difference method. Numerical results obtained by this method are in excellent agreement with finite-difference data.

scholarly journals A new formulation of finite difference and finite volume methods for solving a space fractional convection–diffusion model with fewer error estimates

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Reem Edwan ◽  
Shrideh Al-Omari ◽  
Mohammed Al-Smadi ◽  
Shaher Momani ◽  
Andreea Fulga
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Finite Volume ◽  
Difference Method ◽  
Order Accuracy ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
The Finite Difference Method ◽  
Volume Method

AbstractConvection and diffusion are two harmonious physical processes that transfer particles and physical quantities. This paper deals with a new aspect of solving the convection–diffusion equation in fractional order using the finite volume method and the finite difference method. In this context, we present an alternative way for estimating the space fractional derivative by utilizing the fractional Grünwald formula. The proposed methods are conditionally stable with second-order accuracy in space and first-order accuracy in time. Many comparisons are performed to display reliability and capability of the proposed methods. Furthermore, several results and conclusions are provided to indicate appropriateness of the finite volume method in solving the space fractional convection–diffusion equation compared with the finite difference method.

Comparison Between a Meshless Method and the Finite Difference Method for Solving the Reynolds Equation in Finite Bearings

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Rodrigo Nicoletti
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Meshless Method ◽  
Reynolds Equation ◽  
Normal Force ◽  
Basis Functions ◽  
Structured Meshes ◽  
The Finite Difference Method ◽  
Better Than

Meshless methods are an alternative procedure for solving partial differential equations in opposition to the numerical methods that require structured meshes. In this work, the meshless method with radial basis functions (MMRB) is compared to the finite difference method (FDM) for solving the Reynolds equation applied to lubricated finite bearing applications. The performance of these two methods is compared based on the precision of estimating the normal force applied to the sliding surface of the bearing. Different mesh families are tested for different bearing configurations. Results show that the MMRB is better than the FDM for nonrectangular geometries with coarser meshes. For rectangular domains without discontinuities, the FDM is still the best choice for solving the problem.

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