Potential discontinuity simulations with the numerical Green’s function in steady and transient problems

Abstract

This paper applies the numerical Green’s function (NGF) boundary element formulation (BEM) first in standard form to solve the Laplace equation and then, coupled to the operational quadrature method (OQM), to solve time domain problems (TD-BEM). Both involve the analysis of potential discontinuities in the respective scalar model simulation. The implementation of the associated Green’s function acting as the fundamental solution is advantageous since element discretization of actual discontinuity surfaces are no longer required. In the OQM the convolution integral is substituted by a quadrature formula, whose weights are computed using the fundamental solution in the Laplace domain, producing the direct solution to the problem in the time domain. Applications of the NGF to problems involving the Laplace equation and its transient counterpart are presented for two-dimensional potential flow examples, confirming that the formulation is stable and accurate.