High-resolution ILW outflow boundary treatment for the Navier–Stokes equations

Abstract

WENO schemes have high-resolution and great capability of capturing unsteady and non-linear phenomena. These phenomena occur in elaborated flows, such as cascade and external aerodynamic flows. Thus, high-resolution methods play an important role in modern CFD. Easiness and effectiveness are reached when implementing these methods in rectangular meshes. However, one has the non-boundary-conforming issue. To overcome it the ILW procedure can be employed. We showed that the ILW has a similar behavior to the far-field boundary treatment. Then, we proposed and tested a new ILW outflow boundary treatment and an WENO-type extrapolation. We employed the finite difference method with the positivity-preserving Lax–Friedrichs splitting, high-resolution viscous terms discretization, multi-resolution WENO scheme, and third-order strong stability preserving Runge–Kutta time discretization. We tested the proposed methods in a smooth test case, supersonic flow past a cylinder, NACA 0012 nitrogen flows with 0 and 12° angle of attack, and a NACA 9520 cascade airflow. The proposed methods have high order and resolution, allowed domain size reduction, and captured unsteady and non-linear phenomena. Although preliminary, the NACA 0012 and 9520 flows showed the methods are promising. Common issues with other methods are also reported and further improvements are needed. For example, local mesh refinement, high-order wall boundary treatment, and turbulence modeling.