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A new numerical model for propagation of tsunami waves. (English) Zbl 1140.35529
Summary: A new model for propagation of long waves including the coastal area is introduced. This model considers only the motion of the surface of the sea under the condition of preservation of mass and the sea floor is inserted into the model as an obstacle to the motion. Thus we obtain a constrained hyperbolic free-boundary problem which is then solved numerically by a minimizing method called the discrete Morse semi-flow. The results of the computation in 1D show the adequacy of the proposed model.
MSC:
35L70 Second-order nonlinear hyperbolic equations
47J30 Variational methods involving nonlinear operators
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
74J15 Surface waves in solid mechanics
35R35 Free boundary problems for PDEs
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References:
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