Numerical Method For Shallow Water Equations Based On Central Schemes

The paper summarizes the concerned central schemes for the shallow water equa=tions:Lax-Friedrich scheme,Nessyahu-Tadmor scheme,GS Jiang-D.Levy-CT Lin-S.Osher-E.Tadmor scheme,Central-Upwind scheme,XD Liu-E.Tadmor scheme,R.Sanders-A.Weiser scheme,R.Touma scheme,G.Russo scheme,New scheme and their respective advantages and disadvantagesThe shallow water equations have high re-quirements for their numerical schemes,high resolution numerical schemes often cause oscillations near the shock.If the numerical schemes of the shallow water equations are not positivity preserving,then the calculation process may be interrupted.While satisfying the positivity preserving,it also requires that the scheme is well-balanced.The well-balanced requirement is to solve the pseudo oscillation near the steady state solution.In practical applications,we are more concerned with the behavior in the vicinity of the steady-state solution,especially when the dry and wet interface occurs in the calculation area.It is difficult to design a numerical scheme that is well-balanced and positivity preserving while satisfying high resolution.The core of the paper is to obtain a high resolution central scheme of the well-balanced and positivity preserving by segmenting the source te.rms of the dual-unit shallow water equations and reconstruct-ing the integral of the water depth.We show some of the results of the simulation of the partial schemes by calculating some examples of the one-dimensional shallow water equations and the simulation results of the new scheme.