Table 1: List of numerical test models.
Name Grid size Resolution $t_{\rm end}$ $t_{\rm coll}$ Description

ADO [0, 50] $\times$ [6, 100] 200 $\times$ 400 50.0 - model of Vlahakis et al. (2000), Gracia et al. (2006) and Matsakos et al. (2008)

Models to test the influence of different truncation field lines

FL1 [0, 50] $\times$ [6, 100] 200 $\times$ 400 8.8 5.7 $\alpha_{\rm trunc} = 0.4$ , constant values in external region (analytical values at $[R_{\rm max},Z_{\rm max}]$ )

FL2 [0, 50] $\times$ [6, 100] 200 $\times$ 400 7.3 6.7 $\alpha_{\rm trunc} = 0.8$ , constant values in external region (analytical values at $[R_{\rm max},Z_{\rm max}]$ )

FL3 [0, 50] $\times$ [6, 100] 200 $\times$ 400 10.0 8.1 $\alpha_{\rm trunc} = 5.$ , constant values in external region (analytical values at $[R_{\rm max},Z_{\rm max}]$ )

Models to test the influence of the computational domain

CD1 [0, 50] $\times$ [6, 100] 200 $\times$ 400 6.3 2.7 $\alpha_{\rm trunc} = 0.4$ , in external region damping of $\rho$ and v_z with $\alpha_{\rm trunc}/\alpha$

CD2 [0, 100] $\times$ [6, 200] 200 $\times$ 400 8.9 3.8 same as CD1, but with larger domain (lower resolution, same grid size)

CD3 [0, 100] $\times$ [6, 200] 400 $\times$ 800 8.1 4.1 same as CD1, but with larger domain (same resolution)

CD4 [0, 200] $\times$ [6, 400] 400 $\times$ 800 9.8 6.9 same as CD2, but with even larger domain

CD5 [0, 400] $\times$ [6, 100] 1600 $\times$ 400 4.7 4.5 same as CD1, but with eight times larger domain in R direction, same res.

Models to test different initializations of the external region

ER1 [0, 50] $\times$ [6, 100] 200 $\times$ 400 50.0 24.9 $\alpha_{\rm trunc} = 0.4$ , in external region damping of v_z to constant value

(10% of the value at the truncation field line)

ER2 [0, 50] $\times$ [6, 100] 200 $\times$ 400 3.6 - $\alpha_{\rm trunc} = 0.4$ , in external region damping of all variables with $\exp~ [- (\alpha/\alpha_{\rm trunc})^2 ]$

**Table 1:** List of numerical test models.
Name	Grid size	Resolution	$t_{\rm end}$	$t_{\rm coll}$	Description
ADO	[0, 50] $\times$ [6, 100]	200 $\times$ 400	50.0	-	model of Vlahakis et al. (2000), Gracia et al. (2006) and Matsakos et al. (2008)
Models to test the influence of different truncation field lines
FL1	[0, 50] $\times$ [6, 100]	200 $\times$ 400	8.8	5.7	$\alpha_{\rm trunc} = 0.4$ , constant values in external region (analytical values at $[R_{\rm max},Z_{\rm max}]$ )
FL2	[0, 50] $\times$ [6, 100]	200 $\times$ 400	7.3	6.7	$\alpha_{\rm trunc} = 0.8$ , constant values in external region (analytical values at $[R_{\rm max},Z_{\rm max}]$ )
FL3	[0, 50] $\times$ [6, 100]	200 $\times$ 400	10.0	8.1	$\alpha_{\rm trunc} = 5.$ , constant values in external region (analytical values at $[R_{\rm max},Z_{\rm max}]$ )
Models to test the influence of the computational domain
CD1	[0, 50] $\times$ [6, 100]	200 $\times$ 400	6.3	2.7	$\alpha_{\rm trunc} = 0.4$ , in external region damping of $\rho$ and v_z with $\alpha_{\rm trunc}/\alpha$
CD2	[0, 100] $\times$ [6, 200]	200 $\times$ 400	8.9	3.8	same as CD1, but with larger domain (lower resolution, same grid size)
CD3	[0, 100] $\times$ [6, 200]	400 $\times$ 800	8.1	4.1	same as CD1, but with larger domain (same resolution)
CD4	[0, 200] $\times$ [6, 400]	400 $\times$ 800	9.8	6.9	same as CD2, but with even larger domain
CD5	[0, 400] $\times$ [6, 100]	1600 $\times$ 400	4.7	4.5	same as CD1, but with eight times larger domain in R direction, same res.
Models to test different initializations of the external region
ER1	[0, 50] $\times$ [6, 100]	200 $\times$ 400	50.0	24.9	$\alpha_{\rm trunc} = 0.4$ , in external region damping of v_z to constant value
					(10% of the value at the truncation field line)
ER2	[0, 50] $\times$ [6, 100]	200 $\times$ 400	3.6	-	$\alpha_{\rm trunc} = 0.4$ , in external region damping of all variables with $\exp~ [- (\alpha/\alpha_{\rm trunc})^2 ]$

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