Abstract
A new method of treating incompressible flows with nonslip boundaries is proposed as an extension of the Fourier spectral method. This is characteristic in using the function subspace that is a hyperplane in the Fourier-transformed velocity space, prescribed by the boundary condition, as well as in taking the solenoidal field representation in the Fourier space so that the pressure term need not be involved in the main dynamics and then time-integration can simply be made by the high-order Runge-Kutta scheme. The method can be applied in a more complicated case with an active scalar. As examples, the flow transitions to turbulence in a channel and in a rectangular duct heated from below are treated.
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Hosokawa, I., Yamamoto, K. Conditional Fourier spectral method for direct numerical simulation of incompressible flows. J Sci Comput 10, 271–287 (1995). https://doi.org/10.1007/BF02089952
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DOI: https://doi.org/10.1007/BF02089952