Class of space-time second order accurate high resolution MmB difference schemes in 3D

From the 3D nonlinear hyperbolic conservation laws, the H. Nessyahu and E. Tadmor's methods are developed directly into the 3D cases. The interlace types of Lax-Friedrichs are used as a basic building block and the first order is substituted by the second-order piecewise-linear constant degree approximate. That reduce the excessive numerical viscosity typical to the Lax-Friedrichs forms. By treating the co-derivative separated form properly, a new Riemann-solver-free class of difference schemes is constructed to scalar nonlinear hyperbolic conservation laws for three dimensional flows. It can be proved that, these schemes have second order accurate in space and time domains and satisfy MmB properties under the appropriate CFL limitation. In addition, these schemes can also be extended to the vector systems conservation laws. Finally, several numerical experiments show that the performances of these schemes are quite satisfactory.