A 2D Finite Volume Non-hydrostatic Atmospheric Model ...

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6.3.2 Impact of the corrected divergence dampingTo show how the corrected derivatives in the divergence filter decrease the sensitivity to the choice ofthe damping parameters we consider a simulation without taking mixed second derivatives into account.The parameters £x e 0.001 and £ ze 0.0044 used by Wunderlich in [6] are increased to the default values£x e £ ze 0.05. Therefore, we expect the wind pattern to get smoother. But as can be seen in Figure 6.5this increase almost cancels out the wave pattern when not using the mixed derivatives. This is also inagreement with the statements of Wunderlich in [6]. Nevertheless the remaining wave pattern is nowvery smooth.horizontal velocity u [m/s]vertical velocity w [m/s]1000010000900090008000800070007000height [m]60005000height [m]60005000400040003000300020002000100010000−1 −0.5 0 0.5 1widht [m]x 10 40−1 −0.5 0 0.5 1widht [m]x 10 4Figure 6.5: Horizontal and vertical velocity of a linear, non-<strong>hydrostatic</strong> flow. The contour intervalis 0.001 m/s centered around zero for the vertical and around 10 m/s for the horizontal velocity.Bigger values are solid blue and smaller values are dash-dotted cyan. Mixed derivatives in the divergencedamping term are neglected.However, when we do not neglect the mixed derivatives, as we usually don't, we get results that are ingood agreement with the analytic solution as for example in figure 6.2.6.3.3 Influence of the Rayleigh sponge layerThe Rayleigh sponge layer at the top is introduced to eliminate wave reflections at the boundary and toabsorb upward propagating wave disturbances. To illustrate its effects we made a simulation with thedefault parameters given in table 6.1 but turned off the sponge layer. The results are shown in figure 6.6.Without sponge layer some waves are reflected at the top. They start to propagate downwards and todisturb the solution. Whereas with the sponge layer the waves are filtered out as can be seen in figure6.7.28
x 10 4 relative horizontal velocity u [m/s]x 10 4 relative vertical velocity w [m/s]221.81.81.61.61.41.4height [m]1.210.8height [m]1.210.80.60.60.40.40.20.20−2 −1 0 1 2widht [m]x 10 40−2 −1 0 1 2widht [m]x 10 4Figure 6.6: Horizontal and vertical velocity perturbations for a linear, non-<strong>hydrostatic</strong> flow in thewhole computational domain. No Rayleigh sponge layer at the top. The contour interval is 0.001m/s. Positive values are solid blue and negative values are dash-dotted cyan.x 10 4 relative horizontal velocity u [m/s]x 10 4 relative vertical velocity w [m/s]221.81.81.61.61.41.4height [m]1.210.8height [m]1.210.80.60.60.40.40.20.20−2 −1 0 1 2widht [m]x 10 40−2 −1 0 1 2widht [m]x 10 4Figure 6.7: As figure 6.6, but with Rayleigh sponge layer at the top.29
Page 1: A 2D Finite Volume Non-hydrostatic
Page 5: List of figuresFigure 5.1: Illustra
Page 8 and 9: £¤¢¦§©¡¨¥NomenclatureQDamp
Page 12 and 13: 1.2 MotivationIn [6] Wunderlich imp
Page 15: Cc iR iO'0PPc iPc i/OCc iR ih OO'''
Page 18 and 19: €€€uuG tQ ijt s 0tuww€wwt s
Page 20 and 21: ¼¼µ½¼u¼½u}}}3.5 Reconstructi
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Page 27 and 28: 6
Page 29 and 30: q ijCRJ Zq i , jP 1 Sq p " RJ""q r
Page 31: 5.3 Terrain-following gridThe terra
Page 34 and 35: 6.2 Performance improvementThe main
Page 36 and 37: 6.3 Linear, non-hydrostatic flowWit
Page 40 and 41: 6.3.4 The effects of computational
Page 42 and 43: elative horizontal velocity u [m/s]
Page 44 and 45: vertical velocity w [m/s]8000700060
Page 46 and 47: Figure 6.11: Simulation of a negati
Page 48 and 49: Figure 6.12: Time evolution of maxi
Page 51: References[1] Klemp, J.B., Skamaroc

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