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A Relaxation Scheme for the Two-Layer Shallow Water System

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References

  1. M. Castro, M., Macias, J., Pares, C.: A Q-scheme for a class of systems of coupled conservation laws with source terms. Application to a two-layer 1-D shallow water system, Mathematical Modelling and Numerical Analysis (M2AN), 35, 107–127 (2001)

    MATH  MathSciNet  Google Scholar 

  2. Chapman, S., Cowling, T.G.: The Mathematical Theory of Nonuniform Gases, Cambridge Univ. Press, 3rd Edition, (1970)

    Google Scholar 

  3. Chen, G.-Q., Levermore, D., Liu, T.-P.: Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math., 47, 787–830 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  4. Jin, S., Xin, Z.: The relaxation scheme for systems of conservation laws in arbitrary space dimensions, Comm. Pure Appl. Math., 48, 235–276 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  5. Long, R.R.: Long waves in a two-fluid system, J. Met., 13, 70–74 (1956)

    Google Scholar 

  6. Roe, P.L.: Approximate Riemann solvers, parameter vectors and difference schemes, J. Comp. Phys., 43, 357–372 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  7. Roe, P.L.: Upwind differencing schemes for hyperbolic conservation laws with source terms, Lecture Notes in Math., 1270, 41–51, Springer, Berlin (1987)

    Google Scholar 

  8. Schijf, J.B., Schonfeld J.C.: Theoretical considerations on the motion of salt and fresh water, Proc. of the Minn. Int. Hydraulics Conv., Joint meeting IAHR and Hyd. Div. ASCE. September 1953, 321–333 (1953)

    Google Scholar 

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© 2008 Springer-Verlag Berlin Heidelberg

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Abgrall, R., Karni, S. (2008). A Relaxation Scheme for the Two-Layer Shallow Water System. In: Benzoni-Gavage, S., Serre, D. (eds) Hyperbolic Problems: Theory, Numerics, Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75712-2_11

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