In a hydraulic jump, the supercritical flow suddenly changes to subcritical flow forming steep gradients of flow depth and velocity. In the numerical simulation of this flow, proper grid distribution can play a crucial role in the prediction and resolution of the solutions. In this paper, two different numerical schemes - Mac- Cormack (second-order accurate in space and time) and two-four (fourth-order accurate in space and secondorder accurate in time) -are used with grid adaptation to numerically simulate the hydraulic jump at different Froude numbers in a rectangular channel. Rai and Anderson's method is used to determine the grid speed; however, a different partial differential equation based on the conservative principle of grid arc lengths for clustering the grid points in one-dimensional flow is used along with the Boussinesq equations to simulate the flow.