A novel numerical method for steady-state thermal simulation based on loop-tree and HBRWG basis functions

Abstract

This article presents a novel numerical method for steady-state thermal simulation. This method firstly solves the heat flux efficiently by applying the loop-tree basis functions. Then, the temperature is obtained by finding solutions of the gradient equation. The half boundary Rao-Wilton-Glisson (HBRWG) basis functions are employed for handling arbitrary boundary conditions. In addition, the triangulation-based interpolation technique is utilized to interpolate temperature profile with obtained results in post-processing. Three examples with mixed boundary conditions are studied to validate the accuracy of proposed method for simulating steady-state thermal problems. Numerical results show that our method has a good accuracy and is well capable of handling arbitrary boundary conditions.