A Rapid Steady Solver for the Navier-Stokes Equations

Abstract

Despite the significant advances in algorithms and computer hardware over the years, Computational Fluid Dynamics (CFD) models remain to be very time consuming to compute. For applications where fast turnaround time is required such as in hazard prediction models for the dispersion of airborne contaminants in urban environments, the calculation of the flow field can be a significant bottleneck, and current CFD methods are still too computationally expensive. As a result, state-of-the-art approaches for this application have resorted to diagnostic methods, which although fast, do not contain the complete flow physics. This work bridges this gap through the development of a highly efficient steady-state CFD method that is simple to implement and use. This is through the development of three fundamental elements: an efficient coupled solver for the incompressible Navier-Stokes equations, a mass conservative immersed boundary method, and the use of a zero-equation eddy viscosity turbulence model. Validation tests for urban wind tunnel experiments show that the method is faster than standard CFD methods by over 2 orders of magnitude on the same hardware, with losses of accuracy on the order of 25%. This performance makes it possible to solve useful problems on consumer grade desktop hardware in a matter of minutes.