Numerical schemes for spacing and time are tested to accurately simulate the wave propagation. The tested numerical schemesinclude 2nd-order central differencing, l-order upwind scheme, 2nd-order Leith scheme, 3rd-order MUSCLE, QUICK and QUICKEST schemes in spacing and the Euler and 4th-order Runge-Kutta(R-K) schemes in time. It is seen that more accurate results are expected when the higher-order schemes, especially the schemes combined with a TVD control limiter, are used for solving the wave equation. The 3rd-order upwind scheme with limiter and the 4th-order R-K scheme in tim￡ are finally applied to the wave-making simulation in a digital wave tank.