Toward Construction of Class of Scheme for Navier-Stokes Equations Based on Wavelet Decomposition

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  • Wavelet分解を用いたNavier-Stokes方程式解法スキーム構築の試み(流体工学,流体機械)

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The paper proposes a new class of scheme based on wavelet decomposition of the Navier-Stokes equations and their solutions. The solutions are composed of scaling functions by projecting the nonlinear terms onto the space spanned by the scaling functions. The scheme is first applied to a Riemann problem of the onedimensional inviscid Burgers' equation and the numerical solutions show excellent agreements with the exact one. The scheme is also applied to the Euler equations with the Sod condition, and captures the sharp shock front and the density discontinuity. It is then extended to two-dimension and applied to the cavity flow problems with the Reynolds number up to 20 000. The results, the velocity profile of the centerline at Reynolds number 1 000 in particular, present excellent agreements with the results that are frequently referred to.



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