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.
Domains
Fluid mechanics [physics.class-ph] Atmospheric and Oceanic Physics [physics.ao-ph] Fluid Dynamics [physics.flu-dyn] Computational Physics [physics.comp-ph] Exactly Solvable and Integrable Systems [nlin.SI] Pattern Formation and Solitons [nlin.PS] Analysis of PDEs [math.AP] Classical Analysis and ODEs [math.CA] Numerical Analysis [math.NA]| Origin | Files produced by the author(s) |
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