In my case, v {x y z} is noted as v{1,2,3} respectively. The gravity is on -z direction. The data is only for the core box without ghost cells. The normalization in my code is as follows. The quantities followed by "0" mean the normalized units, namely, length 10 in my data means 10*L0=100microns. ****************************** define normalizations: /* Primary: */ L0 = 1.0000000E-03 cm v0 = 5.0000000E+06 cm/s rho0 = 5.0000000E+00 g/cm^3 /* Derived: */ Time0 = 2.0000000E-10 sec Pressure0 = 1.2500000E+14 dyne/cm^2 = 1.2500000E+02 Mbar Mass0 = 5.0000000E-09 g Atom mass0 = 1.6726000E-24 g acceleration0 = 2.5000000E+16 cm/sec^2 kT0 = atom_mass0*v0^2 = 4.1815000E-11 erg 2.6098490E+01 eV Cv0 = 8.2548129E+07 erg/g-deg Kappa0 = 2.0637032E+12 erg/cm-sec-deg(K) Q0 = 6.2500000E+20 erg/cm^2-sec /* useful values: */ Atom_mass0/Mass0 = 3.3452000E-16 k_B/(Atom_mass v0^2) = 3.3019251E-06 /deg Kappa for T=1: 9.002419537424104E-005 Kappa0 ****************************** ******************* ABLATIVE EQUILIBRIUM ********************* Location of ablation front (mic) = 60.000 Ablation Velocity (mic/ns) = 3.500 Acceleration (mic/ns^2) = 100.000 Edge Temperature (eV) = 1486.827 Values of the heat flux at the bottom (y=0) using two ways HEAT FLUX # 2 (erg/cm^2-sec) = 5.1819941E+21 HEAT FLUX # 3 (erg/cm^2-sec) = 5.1853192E+21 CHECK: The three values of heat flux should be close the Code Will Proceed Using HEAT FLUX # 3 hydro quantities created ******************************