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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.
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Didier Clamond, Denys Dutykh. Non-dispersive conservative regularisation of nonlinear shallow water (and isothermal Euler) equations. Communications in Nonlinear Science and Numerical Simulation, Elsevier, 2018, 55, pp.237-247. ⟨10.1016/j.cnsns.2017.07.011⟩. ⟨hal-01509445v3⟩

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