MATERHORN The immersed boundary method for flow over complex terrain

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1 MATERHORN The immersed boundary method for flow over complex terrain Tina Katopodes Chow, Jingyi Bao, Jason Simon Civil and Environmental Engineering University of California, Berkeley

2 Overview p Field work p Owens Valley rotor simulations p WRF-IBM for mesoscale to microscale n Terra incognita p Log law implementation n Method development and testing n Comparisons with WRF p Application to Granite Mountain n Preliminary results

3 Terra incognita p Push mesoscale models to higher resolution? p Or increase domain size for LES? p Is there a conflict? Meso-scale L ~ km Terra incognita Wyngaard (JAS 2004) LES L < 2 km

4 Challenges in the Terra incognita p Steep topography n Terrain-following coordinate system p Turbulence modeling p Land-surface fluxes similarity theory p Lateral boundary forcing p Other physics parameterizations Meso-scale L ~ km Terra incognita Wyngaard (JAS 2004) LES L < 2 km

5 What we are doing p Weather and Research Forecasting (WRF) model n p Mesoscale to microscale One tool for all scales n n Improved turbulence models for LES Immersed boundary method (IBM) for steep terrain

6 WRF-IBM Framework p Capable as mesoscale or LES code p WRF fails with steep terrain slopes p WRF-IBM (Lundquist et al. 2010, 2012) n WRF + immersed boundary method (IBM) n Same model; just a switch n Nesting possible

7 Increasing resolution steeper slopes 3 km, max slope ~4 1 km, max slope ~ m, max slope ~ m, max slope ~32

8 Terrain slope limit Terrain-following coordinates p Horizontal pressure gradient errors n 45 limit, usually ~30 starts causing problems (e.g. Mahrer 1984) p Grid aspect ratio limitations p Numerical stability

9 Vertical coordinate systems sigma, or terrain-following! Non-orthogonal! eta, or step mountain! orthogonal! immersed boundary! orthogonal! others include sigma-pressure, isentropic, and hybrids!

10 Ghost-cell immersed boundary method Enforce zero velocities on the immersed boundary Nearest neighbors Immersed boundary Ghost point

11 IBM - Boundary reconstruction p IBM implemented in WRF p 2 different interpolation algorithms p Handles highly complex topography Lundquist et al. MWR 2010

12 Inverse distance weighting For complex urban geometries Lundquist et al. 2010, 2012

13 Seamless grid nesting l l l Mesosacle to microscale Must switch from WRF to IBM-WRF When to switch? l Resolution, steepness, aspect ratio, turbulence closure

14 WRF Alone Coarse resolution smooth terrain low error Fine resolution steep terrain high error

15 WRF Alone Coarse resolution smooth terrain low error Fine resolution steep terrain high error

16 IBM-WRF Alone Very coarse resolution grid-scale > mountain-scale (flat plate) low error Coarse resolution large spacing high error (interpolation) Fine resolution small spacing low error

17 IBM-WRF Alone Very coarse resolution grid-scale > mountain-scale (flat plate) low error Coarse resolution large spacing high error (interpolation) Fine resolution small spacing low error

18 IBM-WRF Alone Very coarse resolution grid-scale > mountain-scale (flat plate) low error Coarse resolution large spacing high error (interpolation) Fine resolution small spacing low error

19 WRF to IBM-WRF Switch at intersection for best results Want to develop general guidelines for this curve WRF starts blowing up near 300m resolution on 2D GMAST

20 Complex terrain applications p Current implementation for no-slip n Good for urban environments at ~1 m resolution p Need log law wall stress for complex terrain IBM-WRF for Oklahoma City

21 WRF implementation of log law p Momentum equation in U direction p Requires gradient in

22 WRF implementation of log law

23 IBM log law implementation No-Slip Shear Stress Reconstruction u surface = vsurface = wsurface = 0 τ w U nˆ = 0 κ = µ ln z h 1 z o 2 U u

24 How to validate? p Small changes can make big difference

25 Test Case 1 p Flat plate p Constant eddy viscosity p Top Rayleigh damping layer p Constant shear stress at wall p Analytical solution

26 Test Case 2 p Flat plate p Constant eddy viscosity p Top Rayleigh damping layer p Log law at wall p Analytical solution n Below z1, velocity assumed logarithmic, above linear n Location of z1 determines slope

27 Test Case 2 p Flat plate p Constant eddy viscosity p Top Rayleigh damping layer p Log law at wall p Analytical solution n Below z1, velocity assumed logarithmic, above linear n Location of z1 determines slope

28 Test Case 3 p Flat plate p Constant eddy viscosity p Top Rayleigh damping layer p Log law at wall p Pressure gradient forcing

29 3D log law implementation u I τw u G

30 3D log law implementation τ I τ W τ G

31 Granite Mountain IBM test case Granite Mountain, Utah

fluxes similarity theory DRM and IBM-WRF Meso-scale L ~

32 MATERHORN: addressing challenges in the Terra incognita p Steep topography p Turbulence modeling p Land-surface fluxes similarity theory DRM and IBM-WRF Meso-scale L ~ km Terra incognita Wyngaard (JAS 2004) LES L < 2 km

33 Ongoing work p IBM log law n 3D implementation n Validation p Granite Mountain n Semi-idealized n Real case p Turbulence closure p Owens Valley

Horizontal Mixing in the WRF-ARW Model. Russ Schumacher AT April 2006

Horizontal Mixing in the WRF-ARW Model Russ Schumacher AT 730 5 April 2006 Overview Description of implicit and explicit horizontal mixing in WRF Evaluation of WRF s implicit mixing Model options for explicit