Abstract: The nontraditional method of space time conservation element and solution element (CE/SE), developed by chang S C in 1995, is modified. A new constructing method is used to obtain the calculating schemes. These new schemes not only have all the features which the CE/SE method has, but also are simpler, more accurate and have very high resolution of discontinuities.

Key words: Navier Stokes equations, space-time conservation, numerical method, shock resolution