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In this paper, we develop a new free-stream preserving (FP) method forhigh-order upwind conservative finite-difference (FD) schemes on thecurvilinear grids. This FP method is constrcuted by subtracting a referencecell-face flow state from each cell-center value in the local stencil of theoriginal upwind conservative FD schemes, which effectively leads to areformulated dissipation. It is convenient to implement this method, as it doesnot require to modify the original forms of the upwind schemes. In addition,the proposed method removes the constraint in the traditional FP conservativeFD schemes that require a consistent discretization of the mesh metrics and thefluxes. With this, the proposed method is more flexible in simulating theengineering problems which usually require a low-order scheme for theirlow-quality mesh, while the high-order schemes can be applied to approximatethe flow states to improve the resolution. After demonstrating the strict FPproperty and the order of accuracy by two simple test cases, we considervarious validation cases, including the supersonic flow around the cylinder,the subsonic flow past the three-element airfoil, and the transonic flow aroundthe ONERA M6 wing, etc., to show that the method is suitable for a wide rangeof fluid dynamic problems containing complex geometries. Moreover, these testcases also indicate that the discretization order of the metrics have nosignificant influences on the numerical results if the mesh resolution is notsufficiently large.

Reformulated dissipation for the free-stream preserving of the conservative finite difference schemes on curvilinear grids