Eventos Anais de eventos
COBEM 2019
25th International Congress of Mechanical Engineering
Numerical Solution using SPH Method: An Application to Transient Heat Conduction
Submission Author:
Almério José Venâncio Pains Soares Pamplona , GO
Co-Authors:
Almério José Venâncio Pains Soares Pamplona, Karoliny Freitas Silva, Cláudio Bucar Filho, Joel Vasco
Presenter: Almério José Venâncio Pains Soares Pamplona
doi://10.26678/ABCM.COBEM2019.COB2019-0748
Abstract
The unsteady-state heat conduction on a rectangular plate is analyzed assuming the Dirichlet boundary condition and properties linear behavior such that the superposition hypothesis can be applied. Under these conditions, it is used the Fourier analysis method to find an analytical solution, which is a triple infinite series of sinusoidal functions and an exponential time decreasing function. This solution is used as a reference to further comparisons for two numerical methods used in the present paper. The first mentioned numerical technique is the Smoothed Particle Hydrodynamics method (SPH), which uses particles to model the physical domain of the study object and a kernel function to interpolate the properties of the particles such as temperature, velocity, and density. As a result, there is no need for a numerical mesh, allowing complex geometries modeling. The second technique is the Finite Differential Method (FDM), which has a discrete numerical mesh of the physical domain and a finite difference approach to discretize the governing equations. Both methods are applied to the unsteady-state heat conduction problem, resulting in isothermal curves evolving through the time until they reach the steady-state. Comparing them with the analytical solution, it is found a similar accuracy of order $ 10^{-2} $, although the SPH method has a higher computational cost. Moreover, it is studied the behavior of the particle mass definition equation for SPH under the influence of the smoothed length and the material properties.
Keywords
Transient Heat Conduction, SPH, FDM
