convection theories. Due to its intrinsic drawback, the local MLT cannot handle the convective overshooting consistently. A number of non-local models have been developed to incorporate the feedback of the overshooting on the energy transport in the penetration zone which is neglected in the local MLT. Although these models can produce overshooting, they still consider convection as an extended local phenomenon (see [@roxburgh98] and references therein). In Xiong’s hydrodynamic stellar convection theory (1985b,1989b), the difficulties caused by local treatment disappear spontaneously. Xiong’s calculations show extensive overshooting zones and the kinetic energy fluxes in such zones are negligible. At the same time, the impact on the overall stellar structure is minor (especially for zero-age-main-sequence (ZAMS) stars). However, Xiong’s closure scheme is under debate. Numerical experiments can be used to test the assumptions used in the one-dimensional models. [@roxburgh93] performed a two-dimensional simulation of convective penetration to study the integral constraints on the extent of overshooting by constructing a temperature-dependent radiation conductivity model. [@singh94; @singh95; @singh98] conducted a series of numerical experiments to examine the scaling relationships among the penetration distance ($\Delta_{\rm d}$), vertical velocity at the bottom of the convective region and the total energy flux ($F_{\rm
b}$). The results of 