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

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$Departments of Mathematics and Physics (D-MATH/D ... - RW/CSE$

6.3.4 The effects of computational mixingComputational mixing removes small scale noise of computational origin. Figure 6.8 shows the result ofanother simulation using the default parameters but this time without computational mixing. When wecompare the results to those shown in figure 6.7 above we see, that the computational mixing preventssmall scale disturbances from growing. For example the vertical velocity disturbances on the left side ofthe domain are an effect of the periodic lateral boundary conditions. They are visibly smaller when usingcomputational mixing. Also the solution at the lower boundary is somewhat smoother. The maindrawback of computational mixing is that it also prevents correct wave patterns from growing. Thereforethe amplitude of the mountain waves are slightly closer to the analytic solution when we do not usecomputational mixing.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 6.8: As figure 6.7, but without computational mixing.6.4 Linear hydrostatic flowOur second test case is the simulation of a linear, hydrostatic flow past a Gaussian hill. The Mountainheight H is again 1 m but the mountain half width a is now increased to 5000 m. This yields the non dimensionalmountain height and width ¤h ¥ 0.001 and ‘a e 5 which characterize a linear and hydrostaticflow. We use again the cut-cell approach. The complete list of used parameters is given in table 6.2.Figure 6.9 shows the analytic solution in the steady state compared to the simulation results after 10000seconds. Again, the simulation results are close to the analytic solution.30
parameter value unittime integration schemeatmosphereleapfrogstratified--mountain heightmountain half widthmountain type15000Gaussianmm-horizontal domain sizevertical domain sizehorizontal cell sizevertical cell size rangenumber of horizontal grid cellsnumber of vertical grid cells502150030010070kmkmmm--initial Brunt-Väisälä frequencybottom potential temperatureinitial vertical velocity0.01288101/sKm/stime stepintegration timex-divergence damping coefficientz-divergence damping coefficientAsselin coefficientRayleigh damping coefficientRayleigh damping layer thicknessx-computational mixing coefficientz-computational mixing coefficient0.4100000.050.050.050.0290000.000050.00005ss----m--Table 6.2: Parameters used for the simulation of a linear, hydrostatic flow past a Gaussian hill.31
Page 1: A 2D Finite Volume Non-hydrostatic
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Page 31: 5.3 Terrain-following gridThe terra
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Page 36 and 37: 6.3 Linear, non-hydrostatic flowWit
Page 38 and 39: 6.3.2 Impact of the corrected diver
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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