This study concerns the development of a new method combining high-order CAD-consistent grids and adaptive refinement / coarsening strategies for efficient analysis of compressible flows. The proposed approach allows to use geometrical data from Computer-Aided Design (CAD) without any approximation. Thus, the simulations are based on the exact geometry, even for the coarsest discretizations. Combining this property with a local refinement method allows to start computations using very coarse grids and then rely on dynamic adaption to construct suitable computational domains. The resulting approach facilitates interactions between CAD and Computational Fluid Dynamics (CFD) solvers and focuses the computational effort on the capture of physical phenomena, since geometry is exactly taken into account. The proposed methodology is based on a Discontinuous Galerkin (DG) method for compressible Navier-Stokes equations, modified to use Non-Uniform Rational B-Spline (NURBS) representations. Local refinement and coarsening are introduced using intrinsic properties of NURBS associated to a local error indicator. A verification of the accuracy of the method is achieved and a set of applications are presented, ranging from viscous subsonic to inviscid trans- and supersonic flow problems.

中文翻译：

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使用基于 NURBS 的不连续伽辽金方法的 CAD 一致性自适应细化

本研究涉及开发一种结合高阶 CAD 一致网格和自适应细化/粗化策略的新方法，以有效分析可压缩流。所提出的方法允许使用来自计算机辅助设计 (CAD) 的几何数据而无需任何近似。因此，即使对于最粗略的离散化，模拟也是基于精确的几何形状。将此属性与局部细化方法相结合，允许使用非常粗糙的网格开始计算，然后依靠动态适应来构建合适的计算域。由此产生的方法促进了 CAD 和计算流体动力学 (CFD) 求解器之间的交互，并将计算工作集中在物理现象的捕获上，因为几何被精确地考虑在内。所提出的方法基于用于可压缩 Navier-Stokes 方程的不连续伽辽金 (DG) 方法，并修改为使用非均匀有理 B 样条 (NURBS) 表示。使用与局部误差指标相关的 NURBS 的内在属性引入局部细化和粗化。实现了该方法准确性的验证，并提出了一系列应用，范围从粘性亚音速到无粘性跨音速和超音速流动问题。