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Three-dimensional CIP Solution Method for Navier-Stokes Equation Described with General Coordinate System
Kazuhiro Kohge and Kiyoshi Minemura

The CIP (Cubic Interpolated Pseudo-particle) solution method proposed by Yabe has an established reputation for its computational accuracy and stability as a method to solve the Navier-Stokes equation. Not many applications to three-dimensional complicated flow fields, however, can be found up to new. This paper presents a CIP method transformed for three-dimensional general curvilinear coordinate system. The governing equations transformed from a physical space into a computational space are calculated mainly with contravariant velocities by discretizing them on a staggered arrangement of variables. By applying the method for solving the flows in a three-dimensional cavity space, around a circular cylinder started to move suddenly and in 180° curved pipe, its computation accuracy is confirmed on comparing with the numerical results using a spectral method, measured length of a twin vortex, measured data and the results calculated with QUICK scheme, respectively.

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