Based on the mapping introduced by the classical-map hypernetted-chain (CHNC) method, classical numerical simulations, Monte Carlo and molecular dynamics, have been applied to the twodimensional electron fluid and the results are compared with those of quantum Monte Carlo simulations hitherto reported. It is shown that polarization properties of the ground state obtained by the diffusion Monte Carlo method are reproduced within the accuracy of quantum simulations by both of two mapping functions for the quantum temperature which have been proposed within the CHNC method. These results may serve as the basis of numerical simulations based on the CHNC method which are applicable to finite non-periodic systems like quantum dots and systems at finite temperatures.