A method is proposed for the construction of conservative flow difference schemes that compute compressible viscous gas flows in curvilinear coordinates based on an arbitrary Cartesian Godunov-type scheme. The method is designed for easy use in the sense that the implementation of the scheme in curvilinear coordinates requires only minimal additions to the program code of the basic Cartesian scheme. The scheme construction procedure is illustrated for the case of cylindrical coordinates. A cylindrical scheme is constructed to second order approximation in space. Results of test calculations are reported.
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Translated from Prikladnaya Matematika i Informatika, No. 43, 2013, pp. 25–44.
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Abakumov, M.V. Method for the Construction of Godunov-Type Difference Schemes in Curvilinear Coordinates and its Application to Cylindrical Coordinates. Comput Math Model 25, 315–333 (2014). https://doi.org/10.1007/s10598-014-9228-z
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DOI: https://doi.org/10.1007/s10598-014-9228-z