A NURBS-Enhanced Treatment of Curved Boundary Integrating for the Time-Accurate Upwind Scheme with Unstructured Grids

摘要

In the present paper, the enhanced time-accurate upwind (ETAU) scheme is extended to include a more accurate Non-Uniform Rational B-Spline (NURBS) representation of curved boundary geometry for solving the Euler and Navier-Stokes equation. In the computational domain, for the interior cells a classical ETAU scheme is implemented. For those cells with curved boundaries, the NURBS integrated ETAU scheme (NETAU) is proposed for more accurate fluxes calculation, according to the exact geometry for curved boundary. In the process, special transformation and integration strategy will be introduced to calculate the surface fluxes for curved boundary. The NURBS enhanced geometry description of curved boundary makes the NETAU scheme geometrically flexible and yields an exact expression of complex boundary. Several two-dimensional (2D) numeric tests demonstrate the performance and benefits of NETAU scheme. The results show that this approach provides an more accurate results under same grid of ETAU scheme, at low and high Reynolds number. Meanwhile, the NETAU scheme is still stable for flow with high Mach number. Thus, this method provides a potential bridge to describe complex geometry in computational fluid dynamics (CFD) simulations and is promising to reduce computational cost for accurate simulations of flow fields dominated by sharp edges and high curvature.