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Convergence of AMR and SPH simulations - I. hydrodynamical resolution and convergence tests

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Table 1. Mathematical expressions for the post-shock quantities of the density, ρs, the velocity, vs, andthe sound speed squared, a2s , for isothermal, adiabatic and strong (i.e
Figure 1. Density profiles of 1D adiabatic shocks simulated with SPH and uniform grid for shocks with (a) M′ = 4 at t = 0.8, (b) M′ = 32 at t = 0.1, (c)M′ = 256 at t = 0.0125
Figure 2. Density profiles of 1D isothermal shocks simulated with uniform mesh finite volume at a time1 and 2, whereas the harmonic mean simulations are performed only with t = 0.6 for (a) M′ = 4, (b) M′ = 8, (c) M′ = 16,(d) M′ = 32, and with SPH for (e) M′
Figure 3. Simulations of cooling shocks witharithmetic mean density and (c) SPH using the harmonic mean density; shock density profiles using (d) uniform grid, (e) SPH with the arithmetic mean density M′ = 32 with uniform grid and SPH at t = 4; shock temper
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