Warm bubbles and density current problems solved with a FE Variational Multiscale Compressible solver (VMS-C):




  • 3D warm bubble:
  • Domain: [0:1] x [0:1] x [0:1] km3
  • Resolution: dx=dy=dz=100 meters

Initial steps:

3d_chulisima0000.jpg
3D warm bubble




  • Warm bubble Type 1: as defined in Ahmad and Lindeman 2007 (after Wiker and Skamarok 1998)
  • Domain: [0:20] x [0:10] km2
  • Resolution: dx=dz=50 meters

From top to bottom :
TOP LEFT: Variational Multiscale Compressible (FE, Ref. 3)
TOP RIGHT: WRF-V2, 5th order solution (FD, Ref 1)
BOTTOM LEFT: WRF-V2, 2nd order solution (FD, Ref 1)
BOTTOM RIGHT: f-wave solution (FV, Ref 1)

warm_ahmad_1020s_contourPseudoDetail.jpg
ALYA - CVMS - bilinear elements

5th_wrf.jpg
WRF - 5th order FD solution



warm-ahmad_WRF2ndorder_1020s.jpg
WRF - 2nd order FD solution

warm-ahmad_1020s.jpg
Godunov f-wave (FV). See ref 1




[1] Amhad and Lindeman, 2007 "Euler solutions using flix-based wave decomposition"
[2] Wiker and Skamarock, 1998 "A time-splitting scheme for the elastic equations incorporating second-order Runge-Kutta time differencing"
[3] Marras et al., 2010 "Application of a Galerkin Finite Element Scheme to Atmospheric Buoyant and Gravity Driven Flows" AIAA 48th Aerospace Sciences Meeting, ORlando, FL 4-7 Jan 2010



  • Warm bubble Type 2: as defined in Robert 1993
  • Domain: [0:1.0] x [0:1.5] km2
  • Resolution: dx=dz = 5 meters

robert_smooth_dxdz2_5m_1070s_color.jpg
ALYA 18min: Robert case: VMS solution

robert_18min_2dot5m.jpg
18min: Robert case: Robert reference

robert_smooth_dxdz2_5m_720s_color.jpg
12 min: Robert case: VMS solution

robert_12min_2dot5m.jpg
12 min: Rober case: Reference


Ref:
[1] Robert 1993, "Bubble convection experiements with a semi-implicit formulation of the Euler equations"
[2] Marras et al. "Application of a Variational ...", in preparation


  • Density current: Euler solution without any eddy viscosity added.
  • Domain: [-25.0:25.0] x [0.0:6.0] km2
  • Resolution: dx=dz=50 meters

Top Pair of images:
Contour-line images: Variational multiscale [2]
Color images: f-wave solution [1]





ahmad-densityCurrent_600.jpg
Ahmad f-wave solution: 600s

DENSITY_CURRENT_50m_600s_BW_min10punto39_max26punto5_15contorni.jpg
VMS-C solution: 600s



ahmad-densityCurrent_900.jpg
Godunov f-wave (FV): at 900 s Ref. 1


DENSITY_CURRENT_50mAND100m_4images_legend.jpg
ALYA - CVMS - Bilinear elements, 50m (left ) and 100 m (right)



WRF-densityCurrent-5thorder.jpg
WRF-ARW, 5th order solution


WRF-densityCurrent-2ndorder.jpg
WRF-ARW, 2nd order solution



Ref:
[1] Amhad and Lindeman, 2007 "Euler solutions using flix-based wave decomposition"
[2] Marras et al., 2010 "Application of a Galerkin Finite Element Scheme to Atmospheric Buoyant and Gravity Driven Flows" AIAA 48th Aerospace Sciences Meeting, ORlando, FL 4-7 Jan 2010
[3] Straka et al., 1993 "Numerical solution of a nonlinear density current: a benchmark solution and comparisons"


  • Double bubble (Robert 1993): to study the sensitivity to sharp discontinuities and interaction
doubleb_dx5mdz5m_4images.jpg
ALYA - CVMS - Bilinear elements 10m res.


doubleb_dx5mdz5m_4images_robertRef.jpg
Robert, FD scheme, 10m resolution

Ref:
[1] Robert 1993, "Bubble convection experiements with a semi-implicit formulation of the Euler equations"
[2] Marras et al. "Application of a Variational ...", in preparation