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Modified Finite Volume Nodal Scheme for Euler Equations with Gravity and Friction

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Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 77))

Abstract

In this work we present a new finite volume scheme valid on unstructured meshes for the Euler equation with gravity and friction indeed the classical Godunov type schemes are not adapted to treat the hyperbolic systems with source terms. The new method is based on a finite volume nodal scheme modified to capture correctly the behavior induced by the source terms.

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References

  1. Berthon, C., Turpault, R.: Asymptotic preserving hll schemes. Numer. Methods Partial. Diff. Eqn. 27(6), 1396–1422 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  2. Buet,C., Després, B., Franck, E.: Design of asymptotic preserving schemes for the hyperbolic heat equation on unstructured meshes. Numer. Math. 122(2), 227–278 (2012)

    Google Scholar 

  3. Buet, C., Després, B., Franck, E.: Asymptotic preserving scheme with maximum principle for non linear radiative transfer model on unstructured meshes, C.R. Acad. Sci., Paris, Sér. I, Math., 350(11–12), 633–638 (2012)

    Google Scholar 

  4. Carré, G., Del Pino, S., Després, B., Labourasse, E.: A Cell-centered lagrangian hydrodynamics scheme on general unstructured meshes in arbitrary dimension. JCP. 228(14), 5160–518 (2009)

    Google Scholar 

  5. Chalons, C., Coquel, F., Godlewski, E., Raviart, P-A., Seguin N.: Godunov-type schemes for hyperbolic systems with parameter dependent source. The case of Euler system with friction. M3AS. 20(11), 2109–2166 2010

    Google Scholar 

  6. Chalons C., Girardin M., Kokh S.: Large time step asymptotic preserving numerical schemes for the gas dynamics equations with source terms. SIAM J. Sci. Comput. 35(6), A2874A2902

    Google Scholar 

  7. Gosse, L., Toscani, G.: An asymptotic-preserving well-balanced scheme for the hyperbolic heat equations C. R. Acad. Sci Paris, Ser. I 334, 337–342 (2002)

    Google Scholar 

  8. Greenberg, J., Leroux, A.Y.A.: well balanced scheme for the numerical processing of source terms in hyperbolic equations SIAM J. Numer. Anal 33(1), 1996

    Google Scholar 

  9. Jin S., Levermore D.: Numerical schemes for hyperbolic conservation laws with stiff relaxation terms. JCP. 126,449–467 (1996)

    Google Scholar 

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Correspondence to Emmanuel Franck .

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Franck, E. (2014). Modified Finite Volume Nodal Scheme for Euler Equations with Gravity and Friction. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Springer Proceedings in Mathematics & Statistics, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-05684-5_27

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