Fast boundary-domain integral method for heat transfer simulations

Abstract

In this paper, we present a method to decrease the computational cost of the Boundary-Domain Integral Method. We focus on the solution of the velocity–vorticity formulation of the Navier–Stokes equation for incompressible 3D fluid flow. The objective is to accelerate the solution of the boundary vorticity values. In order to reduce the computational cost of the Boundary-Domain Integral Method, we employ the Adaptive Cross Approximation algorithm in combination with the hierarchical matrix structure. The hierarchical matrix structure enables higher compression rates when individual matrix parts are approximated by low-rank matrices. We use the fundamental solution of the modified Helmholtz equation to improve further the approximation accuracy when solving the boundary vorticity values.The developed algorithm is used to simulate natural convection in a closed cavity. By comparing the simulation results with a published benchmark, we are able to assess the influence of the approximation techniques and give a recommendation on parameter values that lead to optimal compression characteristics when simulating the heat and mass transfer processes.