  In this paper, we develop a new free-stream preserving (FP) method for
high-order upwind conservative finite-difference (FD) schemes on the
curvilinear grids. This FP method is constrcuted by subtracting a reference
cell-face flow state from each cell-center value in the local stencil of the
original upwind conservative FD schemes, which effectively leads to a
reformulated dissipation. It is convenient to implement this method, as it does
not require to modify the original forms of the upwind schemes. In addition,
the proposed method removes the constraint in the traditional FP conservative
FD schemes that require a consistent discretization of the mesh metrics and the
fluxes. With this, the proposed method is more flexible in simulating the
engineering problems which usually require a low-order scheme for their
low-quality mesh, while the high-order schemes can be applied to approximate
the flow states to improve the resolution. After demonstrating the strict FP
property and the order of accuracy by two simple test cases, we consider
various validation cases, including the supersonic flow around the cylinder,
the subsonic flow past the three-element airfoil, and the transonic flow around
the ONERA M6 wing, etc., to show that the method is suitable for a wide range
of fluid dynamic problems containing complex geometries. Moreover, these test
cases also indicate that the discretization order of the metrics have no
significant influences on the numerical results if the mesh resolution is not
sufficiently large.
