Analysis of the Time Increment for the Diffusion Equation with Time-Varying Heat Source from the Boundary Element Method

In this paper a Boundary Element Formulation for the one-dimensional transient heat flow problem is presented. The formulation employs a time-independent fundamental solution; consequently, a domain integral appears in the integral equations, which contains the potential time derivative and the time-dependent heat source term of the governing equation. Linear elements are used for the domain discretization. The time marching scheme is implemented with finite difference approximations. The performance of the formulation was assessed comparing the numerical results with an analytical solution. Convergence of the numerical results is evaluated with varying size time-increment during analysis.