Testing Two Time Marching Schemes for Solving Transient Heat Transfer Problems Using the Boundary Element Method with Direct Interpolation Technique.

Resumo

The boundary element method is one of the main numerical methods used to solve transient heat transfer problems. If a simpler fundamental solution is used, the solution is advanced in time by direct integration schemes based on the first-order finite difference model, normally used with the finite element method. The results obtained with this methodology are satisfactory, but some numerical difficulties are observed in cases where only exclusive Dirichlet conditions are present and also in the calculation of heat fluxes, which are determined directly with the Boundary Element method, due to its mixed formulation. In this work, due to the greater sensitivity of the two-dimensional problems mentioned, two new time-marching schemes are tested: a variation of the well-known Crank-Nicolson scheme and the Houbolt scheme. It is expected that such schemes accurately represent the numerical response of fluxes and temperatures along the time, expanding the range of integration steps suitable for obtaining stable responses, with lower computational cost.