Numerical simulation of the flow around a four-dimensional sphere in a four-dimensional duct

概要

In this report, the flow around a four-dimensional sphere placed in a duct having a four-dimensional rectangular parallelepiped shape is investigated by numerical simulations. The incompressible Navier-Stokes equations with the fourth coordinate and velocity component are used as the basic equations. Fractional step method is employed to solve the equations. For the high Reynolds number flow, the calculation is stabilized by using the third-order accuracy upstream difference for the approximation of the nonlinear term of the Navier-Stokes equations. From the results, it is found that when the Reynolds number is not high, a vortex corresponding to the twin vortex in the case of a cylinder is generated, but its length is shorter than that of a cylinder or a sphere. When the Reynolds number is high, the above vortex becomes unstable and shifts to a new flow and the structure of the flow is remarkable in four-dimensionality.
From the computational results of pressure, it is found that the pressure drag of the four-dimensional sphere is smaller than that of the three-dimensional sphere.

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