Abstract A methodology that combines the advantages of the vertex-centred finite volume (FV) method and high-order hybridisable discontinuous Galerkin (HDG) method is presented for the simulation of the transient inviscid two dimensional flows. The resulting method is suitable for simulating the transient effects on coarse meshes that are suitable to perform steady simulations with traditional low-order methods. In the vicinity of the aerodynamic shapes, FVs are used whereas in regions where the size of the element is too large for finite volumes to provide an accurate answer, the high-order HDG approach is employed with a non-uniform degree of approximation. The proposed method circumvents the need to produce tailored meshes for transient simulations, as required in a low-order context, and also the need to produce high-order curvilinear meshes, as required by high-order methods. Numerical examples are used to test the optimal convergence properties of the combined HDG-FV scheme and to demonstrate its potential in the context of simulating the wind gust effect on aerodynamic shapes.

中文翻译：

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用于模拟瞬态无粘性可压缩流的耦合 HDG-FV 方案

摘要 提出了一种结合顶点中心有限体积(FV)法和高阶可杂化不连续伽辽金(HDG)法优点的瞬态无粘二维流动模拟方法。所得方法适用于模拟粗网格上的瞬态效应，适用于使用传统低阶方法执行稳态模拟。在空气动力学形状附近，使用 FV，而在单元尺寸太大以致于有限体积无法提供准确答案的区域中，使用高阶 HDG 方法，其近似程度不均匀。所提出的方法避免了在低阶环境中需要为瞬态模拟生成定制网格的需要，以及生成高阶曲线网格的需要，根据高阶方法的要求。数值例子用于测试组合 HDG-FV 方案的最佳收敛特性，并证明其在模拟阵风对空气动力学形状的影响的背景下的潜力。