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A good numerical method would be locally mass conservative, produce no or minimal over/under-shoots, produce minimal numerical diffusion, and require no CFL time-step limit for stability. ... Moreover, it would be good for the methods to be of high order accuracy. ... We show how to solve the equations using a global implicit approach in an efficient way, and we present the derived computational results. ...doi:10.1016/j.amc.2014.03.032 fatcat:c527226gyfgbffnq4p67qxd7wi