Simulations of supercritical Hadley circulation, induced by horizontal and vertical temperature gradients imposed on a fluid saturated porous medium layer, are performed numerically. The mathematical model confines the simulation to longitudinal flow in which secondary cell axes are transverse to the direction of the Hadley circulation. Numerical results agree well with critical (bifurcation) states predicted theoretically via linear stability analysis. For horizontal Rayleigh number, Ra-b, smaller than 40 and vertical Rayleigh number, Ra-v, beyond a critical value, results indicate that the flow evolves from subcritical Hadley circulation to supercritical Horton-Rodgers-Lapwood-like flow. A switch in the preferential heat transport direction, from horizontal to vertical, parallels this evolution. For Ra-h beyond 40, numerical simulations at supercritical regime reveal the appearance of a traveling wave characterized by continuous drifting of flow cells in the direction opposite to the applied horizontal temperature gradient, that is towards the cooler temperature.