Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 4 Comparisons of maximum velocity at \(\pmb{y=0.5}\) and \(\pmb{x=0.5}\) with different methods ( \(\pmb{h=\frac{1}{64}}\) , \(\pmb{H=\frac{1}{8}}\) )

From: A variational multiscale method for steady natural convection problem based on two-grid discretization

	SGFEM	OGVMM	TGVMM	Ref. [8]	Ref. [5]	Ref. [24]	Ref. [25]
Ra = 10³
x = 0.5	3.6487	3.64869	3.64902	3.68	-	3.65	3.489
y = 0.5	3.69729	3.69777	3.69732	3.73	-	3.70	3.686
Ra = 10⁴
x = 0.5	16.18	16.1815	16.1928	16.10	15.90	16.18	16.122
y = 0.5	19.6244	19.6317	19.6381	19.90	19.91	19.51	19.79
Ra = 10⁵
x = 0.5	34.7186	34.8201	34.7183	34.00	33.51	34.81	33.39
y = 0.5	68.4705	68.5433	68.5738	70.00	70.60	68.22	70.63

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