A recently developed finite difference-finite volume (FD-FV) approach to solve hyperbolic conservation laws is extended to two-dimensional unstructured grids and its numerical performance is assessed. The FD-FV schemes differ from conventional numerical methods that both nodal values and cell-averaged values are dependent variables and evolved in time. Under this framework, the FD-FV methods: (1) are naturally numerically conservative for cell-averaged values; (2) extend to high-order accuracy straightforwardly; (3) have superior spatial accuracy compared to conventional FD methods and FV methods, for example, a simple two-point upwind discrete differential operator leads to second-order accuracy in space. The previous FD-FV schemes are described in one-dimensional case, and their extensions to multiple dimensions are achieved on structured meshes via tensor product of 1D operators. In this work, the method is extended to two-dimensional triangular meshes; and the numerical performance is assessed by solving subsonic inviscid compressible flow past the NACA 2412 airfoil. Extension to three-dimensional tetrahedral mesh is straightforward.
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