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SUMMARYHealing of nonphysical flow solutions and shock instability from the use of Roe's flux-difference splitting scheme is presented. The proposed method heals nonphysical flow solutions such as the carbuncle phenomenon, the shock instability from the odd-even decoupling problem, and the expansion shock generated from the violated entropy condition. The performance and efficiency of the proposed method are evaluated by solving several benchmark and complex high-speed compressible flow problems.