An accelerated Boundary‐Domain Integral Method for three‐dimensional fluid flow analysis

Abstract

The rapid growth of computer power enables performing of more and more complex numerical simulations. However, the need to develop efficient numerical algorithms is always present. In this study, we propose an acceleration of an algorithm to solve the nonlinear system of Navier-Stokes equations. We present an accelerated Boundary-Domain Integral method (BDIM). The BDIM is a boundary element method (BEM) based method, thus its computational demands scale as O(N 2 ), where N is the number of grid nodes. This is due to the fact that the discretization procedure leads to fully populated matrices. However, the computational demands can be reduced to a linear-logarithmic O(N log N ) complexity, with the implementation of an approximation procedure. In this study, we solve the velocity-vorticity formulation of the Navier-Stokes equations and develop an accelerated algorithm for determination of the boundary vorticity in 3D based on H-matrix and the adaptive cross approximation (ACA) method. We test the algorithm using coupled nanofluid flow and heat transfer. As expected results show that, the acceleration (matrix compression rate) has a negative influence on the solution accuracy.