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Highly energy-conservative finite difference method for the cylindrical coordinate system. (English) Zbl 1178.76260
Summary: A highly energy-conservative second-order-accurate finite difference method for the cylindrical coordinate system is developed. It is rigorously proved that energy conservation in discretized space is satisfied when appropriate interpolation schemes are used. This argument holds not only for an unequally spaced mesh but also for an equally spaced mesh on cylindrical coordinates but not on Cartesian coordinates. Numerical tests are undertaken for an inviscid flow with various schemes, and it turns out that the proposed scheme offers a superior energy-conservation property and greater stability than the intuitive and previously proposed methods, for both equally spaced and unequally spaced meshes.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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