To prevent high-amplitude oscillations in the initial layer, the initial and boundary conditions should be consistent. For definiteness, let the initial conditions be monotonic and decrease faster than any power of $x_in_i$, where $n_i$ is the inward unit normal to the boundary.
I suggest to use anisotropic gaussian distribution for temperature instead of enthalpy. In turn, the initial enthalpy should be computed from temperature.
To prevent high-amplitude oscillations in the initial layer, the initial and boundary conditions should be consistent. For definiteness, let the initial conditions be monotonic and decrease faster than any power of $x_in_i$, where $n_i$ is the inward unit normal to the boundary.