Full Implicit Solution with Scalar-dissipation Finite-volume Approach for Saint-Venant Equations

Based on the conservative form of Saint-Venant equations, the Riemann state value of each physical variable in the cell boundary was reconstructed, and the two order accuracy distribution of each variable in the computational domain was realized. On this basis, the finite-volume method is constructed that the convective fluxes have characteristic with scalar dissipation. In order to describe the real physical function of the relative elevation gradient of water level, extra space discretization is added in the discrete term of relative elevation gradient of water level. This term equal zero at the water region, and can be counteracted the term of Relative elevation gradient of water level at the dry area. Dural time-step algorithm is used to fully implicit discrete the time terms in Saint-Venant equations, therefore the unconditional stability of solution. Finally, 2 typical examples are given to verify the stability and convergence of this new numerical solution.