Compact fourth-order finite volume method for Navier-Stokes equations on staggered grids

December 2, 2008

Time: December 2, 2008
Lecturer: Arpiruk Hokpunna, MSc.
Fachgebiet für Hydromechanik, TU München
Venue: Pfaffenwaldring 61, Raum U1.003 (MML), Universität Stuttgart
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In this talk we present a development of the fourth-order compact scheme in finite volume discretization of the Navier-Stokes equation on staggered grids. A special attention is given to the conservation laws on momentum control volumes. Higher-order divergence-free interpolation for convective velocities ensuring a perfect conservation of mass and momentum on every control volumes is presented. The accuracy of each approximation is studied comparatively on the Fourier space. The importance of higher-order pressure is discussed and numerically validated. Fourth-order accuracy and higher resolution is illustrated by the doubly-periodic shear layers and the instability of a plane channel flow. High resolution property and efficiency of the purposed scheme is demonstrated by a grid dependency study of a direct numerical simulation of a turbulent channel flow. The proposed scheme is highly accurate and efficient. At the same level of accuracy, the purposed scheme is ten-times faster than the second-order scheme. This increasing in efficiency can be spent on a higher resolution gaining more accurate solution at a lower cost.
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