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Numerical wave breaking by a compressible finite volume method

Golay Frédéric, Helluy Philippe, Seguin Nicolas. Numerical wave breaking by a compressible finite volume method. F. Golay P. Helluy N. Seguin. Plan. Mathematical Model Numerical method Test case Numerical result Solitary wave propagation Influence of the pressure law Breaking

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Numerical wave breaking by a compressible finite volume method

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  1. Golay Frédéric, Helluy Philippe, Seguin Nicolas Numerical wave breaking by a compressible finite volume method

  2. F. Golay P. Helluy N. Seguin Plan • Mathematical Model • Numerical method • Test case • Numerical result • Solitary wave propagation • Influence of the pressure law • Breaking • Shallow water model • Conclusion

  3. F. Golay P. Helluy N. Seguin Mathematical model ( ) = g j - re - g j p j p ( ) 1 ( ) ( ) 1 1 1 g + p ( p ) = j + j - ( 1 ) = c g j - g - g - ( ) 1 1 1 r w a g j p j g p g p ( ) ( ) w w a a = j + j - ( 1 ) g j - g - g - ( ) 1 1 1 w a where Sound velocity Equation Of State: stiffened gaz (Abgrall-Saurel, 1996)

  4. F. Golay P. Helluy N. Seguin Numerical model Ci Cj The system has the form of a system of conservation laws We solve it by a standard finite volume scheme • Second order extension:MUSCL • No pressure oscillation thanks to a special non-conservative discretisation of the fraction evolution.

  5. F. Golay P. Helluy N. Seguin Test Case In the air sound velocity c=20m/s, p=105 Pa pa=-99636 Pa, ga=1.1 In the water sound velocity c=20m/s, p=105 Pa pw=263636 Pa, gw=1.1

  6. F. Golay P. Helluy N. Seguin Numerical results: solitary wave propagation 1/2 Mesh: 2000x150 Initial velocity

  7. F. Golay P. Helluy N. Seguin Numerical results: solitary wave propagation 2/2 Kinetic energie

  8. F. Golay P. Helluy N. Seguin Numerical results: Influence of the pressure law 1/2 Mesh 100x20 horizontal velocity*density c=20 m/s c=100 m/s c=400 m/s

  9. F. Golay P. Helluy N. Seguin Numerical results: Influence of the pressure law 2/2 Mesh 100x20 vertical velocity*density c=20 m/s c=100 m/s c=400 m/s

  10. F. Golay P. Helluy N. Seguin Breaking 1/2

  11. F. Golay P. Helluy N. Seguin Breaking 2/2

  12. F. Golay P. Helluy N. Seguin Shallow water model 1/2

  13. F. Golay P. Helluy N. Seguin Shallow water model 2/2

  14. F. Golay P. Helluy N. Seguin Conclusion • Simple and efficient method: no tracking of the interface, • The same code can be used for compressible multifluid flows. • Improvements: • Automatic mesh refinement, • Low Mach preconditionning for more physical results, • Dispersive model for the shallow water model.

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