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The positivity-preserving scheme for the flux reconstruction (FR) framework is studied in this paper. A simple and direct implementation of the scheme is also proposed. Owing to the scheme and the implementation, FR or other high-order nodal methods can provide completely physically meaningful solutions at each time step. Their robustness is greatly enhanced. In the numerical tests, the solving of Euler equations coupled with artificial viscosity and Navier-Stokes equations is focused. Satisfying results are obtained in problems that include strong shocks or vacuum states.