SOLUTION OF TRANSIENT DIFFUSIVE PROBLEMS USING THE DIRECT INTERPOLATION TECHNIQUE (Atena Editora)

Abstract

The stability of the transient response of BEM (boundary element method) formulations, which use time-independent fundamental solutions, such as the double reciprocity formulation (DEM), is its greatest numerical difficulty. The coupling of direct integration schemes from the finite difference method with the boundary discretization model implies restrictions on the value of the time step. This means that such values are located within a limited range, and cannot be too large due to lack of consistency in the response, nor too small, as instability is produced. Recently, an alternative formulation called the direct interpolation method (MECID) was proposed, which uses the same radial interpolation functions as the MECDR, but approximating the entire core of the domain integral of the transient term. Since MECID has been shown to be more robust than MECDR, this work presents comparative simulations between the two formulations. The transient heat conduction problem was chosen due to its simplicity compared to dynamic problems. However, in these cases, restrictions related to the recommended range of integration interval are also observed, allowing to infer whether there is progress in the use of MECID in relation to MECDR.