A Stable Numerical Method for the Time Dependent Navier-Stokes Equations and Its Application in Street Canyon Flows

Abstract

The flow over street canyon with different configurations is simulated us¬ing the time dependent Navier-Stokes equations. A three-step fractional method [1] is used to solve the velocity field and the pressure field separately from the governing equations. In the first step of the fractional method, the intermediate velocity components, which do not satisfy the continuity equation, are firstly computed from the momentum equations with the pressure terms dropped. Next, the pressure field is obtained from the pressure Poisson equation. In the third step, the velocities are updated based on the pressure obtained from the sec¬ond step. An eight-node isoparametric element with bi-quadratic interpolation for velocity and bi-linear interpolation for pressure over an element is used to discretise the space domain. The convective terms are discretised using the second order Adams-Bashforth scheme. The Streamline Upwind Petrov-Galerkin (SUPG) technique is introduced to prevent numerical oscillations for flows at high Reynolds numbers. The wind field model is validated by simulating a backward-facing step flow within a wide range of Reynolds numbers. The dynamical characteristics of the simulated flow have excellent agreement with the experimental data [2] at Reynolds numbers lower than 600 and higher than 1500. For Reynolds numbers between 600 and 1500, it is generally difficult to predict precisely in a numerical way due to the complexity of the transitional flow.