A Thermal Conduction Comparative Study Between the FDM  and SPH Methods with A Proposed C++ Home Code

Mohammed Bensafi; Belkacem Draoui; Younes Menni; Houari Ameur

Authors

Mohammed Bensafi Laboratory of Energy in Arid Areas (ENERGARID), University of Bechar, P.O. Box 417, Bechar 08000, Algeria
Belkacem Draoui Laboratory of Energy in Arid Areas (ENERGARID), University of Bechar, P.O. Box 417, Bechar 08000, Algeria
Younes Menni Unit of Research on Materials and Renewable Energies, Department of Physics, Faculty of Sciences, Abou Bekr Belkaid University, P.O. Box 119, Tlemcen 13000, Algeria
Houari Ameur Department of Technology, University Centre of Naama – Ahmed Salhi, P.O. Box 66, Naama, 45000, Algeria

Keywords:

Thermal conduction, Finite difference method, Smoothed particle hydrodynamic, C code

Abstract

The heat transfer phenomenon is modeled by the Finite Difference Method (FDM) and the Soothed Particle Hydrodynamic (SPH) approach. The numerical approach under investigation may be used to solve many complex problems of applied mechanics. The Finite Element Method (FEM) is generally used for the Lagrangian description, and the FDM is used for the Eulerian report. However, the SPH method, which is better than other approaches to solve some problems, may be used in many aspects. Numerical details on the SPH method are discussed in this paper, with a focus on its application on the heat equation. A simple two-dimensional heat conduction problem is simulated by using the SPH approximation procedure and the newly constructed quartic smoothing function. Besides, a comparison is made between both techniques. Finally, C++ code is proposed for SPH and FDM methods.