Table 2: Numerical parameters of galaxy test runs. Tabulated are the model label (1), and the input parameters: the number of particles (2), the softening parameter $\varepsilon$ (3), and the time step $\Delta t$ (4). The units of length and time are $40~{\mbox {kpc}}$ and $250~{\mbox {Myr}}$ , respectively. As a result of simulations the following control parameters are displayed: the relative change of components of the disc velocity dispersions (5-7), the disc angular momentum loss (8), the Toomre's Q parameter (9), the Toomre's X parameter (10), the average value of the distortion parameter (11), the conservation of the total energy (12) and the total angular momentum (13) of the system. Finally, we mention the code used (14).
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)

Model N $\varepsilon$ $\Delta t$ $\gamma_r$ $\gamma_{\varphi}$ $\gamma_{z}$ $\frac{\Delta L_{{\rm d}}}{L_{{\rm d 0}}}, \%$ Q X₂ ${\overline \eta}$ $\frac{\Delta E}{E_0},\%$ $\frac{\Delta L}{L_0}, \%$ Code

A01 40 960 0.025 1/512 0.782 0.452 0.815 1.5 2.0 2.0 0.065 0.01 0.13 GBSPH

A02 - 0.020 1/512 0.670 0.623 1.115 2.1 2.1 2.3 0.033 0.01 0.05 -

A03 - 0.015 1/512 0.806 0.792 1.089 2.4 2.5 1.5 0.036 0.01 0.12 -

A04 - 0.010 1/512 0.824 0.605 1.131 3.2 2.5 1.0 0.029 0.03 0.19 -

A05 - 0.005 1/512 0.863 0.676 1.249 4.5 2.8 0.9 0.026 0.04 0.19 -

A06 - 0.001 1/512 0.817 0.866 1.374 6.4 3.0 0.8 0.025 2.13 0.12 -

A07 163 840 0.015 1/512 0.457 0.335 0.446 0.8 1.9 2.5 0.021 0.01 0.02 -

A08 - 0.010 1/512 0.541 0.443 0.532 1.0 2.2 2.5 0.019 0.01 0.02 -

A09 - 0.005 1/512 0.573 0.417 0.662 1.3 2.3 2.0 0.015 0.02 0.05 -

A10 - 0.001 1/512 0.679 0.556 0.909 2.8 2.6 1.5 0.016 0.57 0.03 -

A11 - 0.010 1/64 0.562 0.398 0.477 1.2 2.1 2.0 0.019 1.08 0.07 -

A12 - 0.010 1/128 0.527 0.397 0.466 1.0 2.1 2.0 0.017 0.04 0.05 -

A13 - 0.010 1/256 0.536 0.462 0.470 1.1 2.2 2.5 0.019 0.02 0.02 -

A14 - 0.010 1/512 0.541 0.443 0.532 1.0 2.2 2.5 0.019 0.01 0.02 -

A15 - 0.010 1/1024 0.523 0.482 0.478 1.2 2.2 2.2 0.025 0.02 0.05 -

A16 491 520 0.010 1/512 0.347 0.269 0.195 0.6 1.9 2.6 0.016 0.01 0.04 -

A17 - 0.008 1/512 0.386 0.224 0.263 0.5 2.0 2.8 0.012 0.01 0.02 -

A18 - 0.006 1/512 0.384 0.270 0.277 0.6 2.0 2.8 0.011 0.01 0.02 -

A19 - 0.004 1/512 0.340 0.277 0.316 0.7 2.1 2.8 0.009 0.02 0.02 -

A20 - 0.002 1/512 0.333 0.253 0.382 0.7 2.2 2.7 0.008 0.04 0.03 -

A21 - 0.001 1/512 0.315 0.256 0.455 0.8 2.2 2.6 0.008 0.21 0.03 -

A22 655 360 0.008 1/512 0.320 0.247 0.155 0.4 1.9 2.8 0.010 0.02 0.01 -

A23 - 0.001 1/512 0.306 0.253 0.389 0.7 2.1 2.5 0.009 0.12 0.02 -

A24 163 840 0.015 1/512 0.786 0.618 0.536 2.0 2.4 2.4 0.035 0.09 0.02 GADGET

A25 - 0.010 1/512 0.861 0.648 0.566 2.6 2.5 2.1 0.030 0.12 0.06 -

A26 - 0.005 1/512 0.600 0.477 0.708 2.0 2.5 1.9 0.016 0.13 0.05 -

A27 - 0.001 1/512 0.658 0.529 0.908 2.5 2.6 1.4 0.014 0.79 0.05 -

A28 655 360 0.008 1/512 0.674 0.505 0.271 1.3 2.1 2.6 0.018 0.21 0.57 -

A29 - 0.001 1/512 0.308 0.276 0.425 0.6 2.2 2.7 0.008 0.30 0.42 -

A30 1 310 720 0.006 1/512 0.369 0.276 0.141 0.3 2.0 3.1 0.010 0.11 0.29 -

A31 - 0.001 1/512 0.267 0.229 0.312 0.5 2.1 2.8 0.008 0.13 1.11 -

**Table 2:** Numerical parameters of galaxy test runs. Tabulated are the model label (1), and the input parameters: the number of particles (2), the softening parameter $\varepsilon$ (3), and the time step $\Delta t$ (4). The units of length and time are $40~{\mbox {kpc}}$ and $250~{\mbox {Myr}}$ , respectively. As a result of simulations the following control parameters are displayed: the relative change of components of the disc velocity dispersions (5-7), the disc angular momentum loss (8), the Toomre's Q parameter (9), the Toomre's X parameter (10), the average value of the distortion parameter (11), the conservation of the total energy (12) and the total angular momentum (13) of the system. Finally, we mention the code used (14).
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)
Model	N	$\varepsilon$	$\Delta t$	$\gamma_r$	$\gamma_{\varphi}$	$\gamma_{z}$	$\frac{\Delta L_{{\rm d}}}{L_{{\rm d 0}}}, \%$	Q	X₂	${\overline \eta}$	$\frac{\Delta E}{E_0},\%$	$\frac{\Delta L}{L_0}, \%$	Code
A01	40 960	0.025	1/512	0.782	0.452	0.815	1.5	2.0	2.0	0.065	0.01	0.13	GBSPH
A02	-	0.020	1/512	0.670	0.623	1.115	2.1	2.1	2.3	0.033	0.01	0.05	-
A03	-	0.015	1/512	0.806	0.792	1.089	2.4	2.5	1.5	0.036	0.01	0.12	-
A04	-	0.010	1/512	0.824	0.605	1.131	3.2	2.5	1.0	0.029	0.03	0.19	-
A05	-	0.005	1/512	0.863	0.676	1.249	4.5	2.8	0.9	0.026	0.04	0.19	-
A06	-	0.001	1/512	0.817	0.866	1.374	6.4	3.0	0.8	0.025	2.13	0.12	-
A07	163 840	0.015	1/512	0.457	0.335	0.446	0.8	1.9	2.5	0.021	0.01	0.02	-
A08	-	0.010	1/512	0.541	0.443	0.532	1.0	2.2	2.5	0.019	0.01	0.02	-
A09	-	0.005	1/512	0.573	0.417	0.662	1.3	2.3	2.0	0.015	0.02	0.05	-
A10	-	0.001	1/512	0.679	0.556	0.909	2.8	2.6	1.5	0.016	0.57	0.03	-
A11	-	0.010	1/64	0.562	0.398	0.477	1.2	2.1	2.0	0.019	1.08	0.07	-
A12	-	0.010	1/128	0.527	0.397	0.466	1.0	2.1	2.0	0.017	0.04	0.05	-
A13	-	0.010	1/256	0.536	0.462	0.470	1.1	2.2	2.5	0.019	0.02	0.02	-
A14	-	0.010	1/512	0.541	0.443	0.532	1.0	2.2	2.5	0.019	0.01	0.02	-
A15	-	0.010	1/1024	0.523	0.482	0.478	1.2	2.2	2.2	0.025	0.02	0.05	-
A16	491 520	0.010	1/512	0.347	0.269	0.195	0.6	1.9	2.6	0.016	0.01	0.04	-
A17	-	0.008	1/512	0.386	0.224	0.263	0.5	2.0	2.8	0.012	0.01	0.02	-
A18	-	0.006	1/512	0.384	0.270	0.277	0.6	2.0	2.8	0.011	0.01	0.02	-
A19	-	0.004	1/512	0.340	0.277	0.316	0.7	2.1	2.8	0.009	0.02	0.02	-
A20	-	0.002	1/512	0.333	0.253	0.382	0.7	2.2	2.7	0.008	0.04	0.03	-
A21	-	0.001	1/512	0.315	0.256	0.455	0.8	2.2	2.6	0.008	0.21	0.03	-
A22	655 360	0.008	1/512	0.320	0.247	0.155	0.4	1.9	2.8	0.010	0.02	0.01	-
A23	-	0.001	1/512	0.306	0.253	0.389	0.7	2.1	2.5	0.009	0.12	0.02	-
A24	163 840	0.015	1/512	0.786	0.618	0.536	2.0	2.4	2.4	0.035	0.09	0.02	GADGET
A25	-	0.010	1/512	0.861	0.648	0.566	2.6	2.5	2.1	0.030	0.12	0.06	-
A26	-	0.005	1/512	0.600	0.477	0.708	2.0	2.5	1.9	0.016	0.13	0.05	-
A27	-	0.001	1/512	0.658	0.529	0.908	2.5	2.6	1.4	0.014	0.79	0.05	-
A28	655 360	0.008	1/512	0.674	0.505	0.271	1.3	2.1	2.6	0.018	0.21	0.57	-
A29	-	0.001	1/512	0.308	0.276	0.425	0.6	2.2	2.7	0.008	0.30	0.42	-
A30	1 310 720	0.006	1/512	0.369	0.276	0.141	0.3	2.0	3.1	0.010	0.11	0.29	-
A31	-	0.001	1/512	0.267	0.229	0.312	0.5	2.1	2.8	0.008	0.13	1.11	-

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