Abstract
In this paper, a single high-order compact flowfield-dependent variation (HOC-FDV) method is developed, valid for twodimensional inviscid compressible as well as incompressible flow problems. The method has third-order accuracy in time and fourth-order accuracy in space. The FDV scheme is used for time discretization and the fourth-order compact Pade scheme is used for spatial derivatives. The solution procedure consists of a number of tri-diagonal matrix operations and produces an accurate solver. Numerical examples are solved to demonstrate the accuracy and convergence characteristics of the high-resolution scheme. The test cases are flow over a compression corner, a channel flow with compression/expansion, and a flow past NACA 0012 airfoil. The numerical results show an excellent agreement with analytical and published numerical results and they clearly demonstrate the higher accuracy of a single HOC-FDV scheme for both incompressible and compressible flows.
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