A method is proposed for the construction of conservative flow difference schemes for the calculation of compressible viscous gas flows in curvilinear coordinates based on an arbitrary Godunov-type Cartesian scheme. The realization of the scheme in curvilinear coordinates requires minimal additions to the basic Cartesian scheme code. The method is illustrated in application to the case of spherical coordinate. A spherical scheme of second-order spatial approximation is constructed. Results of test calculations are reported.
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Translated from Prikladnaya Matematika i Informatika, No. 45, 2014, pp. 63–83.
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Abakumov, M.V. Construction of Godunov-Type Difference Schemes in Curvilinear Coordinates and an Application to Spherical Coordinates. Comput Math Model 26, 184–203 (2015). https://doi.org/10.1007/s10598-015-9267-0
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DOI: https://doi.org/10.1007/s10598-015-9267-0