Highly energy-conservative finite difference method for the cylindrical coordinate system
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 schemed, 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 scheme,,,, 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. (C) 2002 Elsevier Science (USA).
finite difference method cylindrical coordinate system energy conservation pipe flow incompressible flow advection body force singularity