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Applying high-order finite-difference schemes, like the extensively usedlinear-upwind or WENO schemes, to curvilinear grids can be problematic. Thegeometrically induced error from grid Jacobian and metrics evaluation canpollute the flow field, and degrade the accuracy or cause the simulationfailure even when uniform flow imposed, i.e. free-stream preserving problem. Inorder to address this issue, a method for general linear-upwind and WENOschemes preserving free-stream on stationary curvilinear grids is proposed.Following Lax-Friedrichs splitting, this method rewrites the numerical fluxinto a central term, which achieves free-stream preserving by using symmetricalconservative metric method, and a numerical dissipative term with a localdifference form of conservative variables for neighboring grid-point pairs. Inorder to achieve free-stream preservation for the latter term, the localdifference are modified to share the same Jacobian and metric terms evaluatedby high order schemes. In addition, a simple hybrid scheme switching betweenlinear-upwind and WENO schemes is proposed of improving computationalefficiency and reducing numerical dissipation. A number of testing casesincluding free-stream, isentropic vortex convection, double Mach reflection andflow past a cylinder are computed to verify the effectiveness of this method.

Free-stream preserving linear-upwind and WENO schemes on curvilinear grids