Incorporation of NURBS Boundary Representation with an Unstructured Finite Volume Approximation (Communications in Computational Physics, 2018)
For compressible flow computations, the present paper extends the ETAU(enhanced time-accurate upwind) unstructured finite volume (FV) scheme to handlecurved domain boundary with better accuracy. For the interior cells in the computationaldomain or the boundary cells with straight line boundary, the original ETAUscheme with second order accuracy in space and time is applied. For those boundarycells with the curved geometry, a more accurate Non-Uniform Rational B-Spline(NURBS) representation of the boundary is considered. The NURBS is commonly employedin computer aided design (CAD) to construct complex geometries. Here, ityields an exact geometry expression of complex boundary geometry. By combiningETAU with NURBS, the NURBS incorporated ETAU scheme (NETAU) is proposed formore accurate geometrical representation and fluxes evaluation. Details of the computingprocedure of the geometry and surface fluxes for cells on the curved boundary,such as special transformation strategies and merging of ETAU and NURBS, areintroduced and implemented. With NURBS, the NETAU scheme are geometricallyversatile and more flexible. Several two-dimensional (2D) numerical cases are investigatedto demonstrate the performance, computing efficiency and benefits of the NETAUscheme. The numerical results show that, for flows with low speed and highReynolds number, the NETAU scheme provides more accurate pressure distributionon curved boundary than the original ETAU scheme. Meanwhile, the high-speed flowcase shows that the NETAU scheme is still stable for high Mach number problem withshocks. Thus, the NETAU scheme potentially provides an accurate tool to describecomplex geometry in computational fluid dynamics (CFD) simulations. It will helpto reduce computational costs and enhances accuracy for flow domain dominated bycomplex geometries, with features such as high curvature and sharp edges.