Title: Non-dispersive conservative regularisation of nonlinear shallow water (and isothermal Euler) equations,
Abstract: A new regularisation of the shallow water (and isentropic Euler) equations is
proposed. The regularised equations are non-dissipative, non-dispersive and
possess a variational structure. Thus, the mass, the momentum and the energy
are conserved. Hence, for instance, regularised hydraulic jumps are smooth and
non-oscillatory. Another particularly interesting feature of this
regularisation is that smoothed `shocks' propagates at exactly the same speed
as the original discontinuous ones. The performance of the new model is
illustrated numerically on some dam-break test cases, which are classical in
the hyperbolic realm.