Application of smoothed particle hydrodynamics method in two-dimensional heat equation

Abstract

Solution to the two-dimensional (2D) heat equation has been done by many researchers earlier. Numerical methods always being used in solving 2D heat equation. The usual numerical method being chosen is the finite difference techniques such as explicit finite difference method, Crank-Nicolson method and alternating direction implicit (ADI) method. However, in this research, the smoothed particle hydrodynamics (SPH) method is chosen and being studied to be applied in solving the 2D heat equation. The algorithm for SPH method is also being developed. As for making the comparisons to study on the accuracy of SPH method, 2D heat equation also being solved using ADI method. FORTRAN programming is used as a calculation medium for both the ADI and SPH method.