2次元マントル対流計算基本コード (その1)
ベンチマークテストの結果

以下の場合について、 Blankenbach et al. (1989) とのベンチマークテストを行なった。 図に、64×64メッシュで計算した(a) 温度分布、(b) 流線を示す。

Case 1a
Case 1b
Case 1c
Case 2a
Case 2b

まとめ

• Case 1a (constant viscosity; Ra=10⁴)

  mesh	Nu	Vrms	q1(=q3)	q2(=q4)
  16x16	4.72688489	41.7552172	7.69542605	0.887088466
  32x32	4.840006	42.5601175	7.96660508	0.66492677
  64x64	4.87274487	42.7854408	8.03604387	0.608154243
  32x16	4.77484486	42.0426309	7.72113164	0.778424673
  16x32	4.78906415	42.2640866	7.94019735	0.772623789
  Bl.	4.884409	42.864947	8.059384	0.588810

• Case 1b (constant viscosity; Ra=10⁵)

  mesh	Nu	Vrms	q1(=q3)	q2(=q4)
  16x16	9.23554957	181.183463	14.4245198	3.44128269
  32x32	10.0826079	189.192181	17.7643222	1.42555284
  64x64	10.3947858	191.985327	18.7311975	0.898252325
  32x16	9.49190528	183.927789	14.7679245	2.93537791
  16x32	9.75382495	185.922438	17.2252972	2.01140043
  Bl.	10.534095	193.21454	19.079440	0.722751

• Case 1c (constant viscosity; Ra=10⁶)

  mesh	Nu	Vrms	q1(=q3)	q2(=q4)
  16x16	13.5055924	675.694693	16.6358113	9.8363381
  32x32	18.9630025	780.809445	31.2146299	6.94187899
  64x64	20.8844492	814.692889	41.4424521	2.47772268
  32x16	13.8799096	685.204795	17.5335681	9.47613416
  16x32	17.8035548	756.843997	27.7273038	7.86542413
  Bl.	21.972465	833.98977	45.96425	0.432202

• Case 2a (temperature-dependent viscosity)

  mesh	Nu	Vrms	q1	q2	q3	q4
  16x16	10.5027427	363.805214	17.4007895	2.37770447	14.4686945	7.0549197
  32x32	10.6328654	446.323732	21.7691418	1.11814854	20.7018343	4.26535748
  64x64	10.1323199	473.596368	18.2315411	1.03379525	25.0599327	1.55482703
  32x16	10.9022077	360.023914	18.3097793	1.88424844	15.5677382	6.70204636
  16x32	9.95035059	452.255886	19.01072	1.4775106	17.3608716	4.88921834
  Bl.	10.0660	480.4334	17.53136	1.00851	26.8085	0.497380

• Case 2b (temperature- and depth-dependent viscosity)

  mesh	Nu	Vrms	q1	q2	q3	q4
  16x16	6.67643566	189.381658	14.9503093	0.751449451	10.2234025	4.13969333
  32x32	6.8959977	178.637147	23.3963087	0.28416789	11.7673163	2.10061912
  64x64	6.95458945	176.149653	20.4355267	0.213725446	13.366983	1.134206
  32x16	6.5542687	171.917327	17.1211287	0.344177344	9.74542626	3.26583464
  16x32	6.98232674	199.991457	17.0446054	0.698036959	12.6369991	3.21381544
  Bl.	6.9299	171.755	18.4842	0.17742	14.1682	0.61770

参考文献

• Blankenbach, B., F. Busse, U. Christensen, L. Cserepes, D. Gunkel, U. Hansen, G. Jarvis, M. Koch, G. Marquatt, D. Moore, P. Olson, H. Schmeling, anf T. Schnaubelt, A benchmark comparison for mantle convection codes, Geophys. J. Int., 98, 23-38, 1989. [doi:10.1111/j.1365-246X.1989.tb05511.x]