Convective hydrocodes for radial stellar pulsation. Physical and   numerical formulation
  In this paper we describe our convective hydrocodes for radial stellar pulsation. We adopt the Kuhfuss (1986) model of convection, reformulated for the use in stellar pulsation hydrocodes. Physical as well as numerical assumptions of the code are described in detail. Described tests show, that our models are numerically robust and reproduce basic observational constraints.   We discuss the effects of different treatment of some quantities in other pulsation hydrocodes. Our most important finding concerns the treatment of the turbulent source function in convectively stable regions. In our code we allow for negative values of source function in convectively stable zones, which reflects negative buoyancy. However, some authors restrict the source term to non-negative values. We show that this assumption leads to very high turbulent energies in convectively stable regions. The effect looks like overshooting, but it is not, because turbulence is generated by pulsations. Also, turbulent elements do not carry kinetic nor thermal energy, into convectively stable layers. The range of this artificial overshooting (as we shall call it) is as large as 6 local pressure scale heights, leading to unphysical internal damping through the eddy-viscous forces, in deep, convectively stable parts of the star. 
R. Smolec and P. Moskalik