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.
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