Acceleration of a BEM based solution of the velocity-vorticity formulation of the Navier-Stokes equations by the cross approximation method

The developed algorithm is tested using the Arnold-Beltrami-Childress and lid driven cavity flows. We study the accuracy of boundary vorticity estimation and of the flow solution for different flow complexities (Reynolds number values), computational mesh densities and cross approximation settings. We found that that by using the cross approximation technique in the flow solver, we were able to reduce the computational demands of storing matrices to approximately 30% of the storage space of the original matrices. Furthermore, we showed that achieved approximation extent depends on the complexity of the simulated flow problem.