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A conservative, weakly nonlinear semi-implicit finite volume scheme for the compressible Navier−Stokes equations with general equation of state

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  • Dumbser, Michael
  • Casulli, Vincenzo

Abstract

In the present paper a new efficient semi-implicit finite volume method is proposed for the solution of the compressible Euler and Navier−Stokes equations of gas dynamics with general equation of state (EOS). The discrete flow equations lead to a mildly nonlinear system for the pressure, containing a diagonal nonlinearity due to the EOS. The remaining linear part of the system is symmetric and at least positive semi-definite. Mildly nonlinear systems with this particular structure can be very efficiently solved with a nested Newton-type technique.

Suggested Citation

  • Dumbser, Michael & Casulli, Vincenzo, 2016. "A conservative, weakly nonlinear semi-implicit finite volume scheme for the compressible Navier−Stokes equations with general equation of state," Applied Mathematics and Computation, Elsevier, vol. 272(P2), pages 479-497.
    • Handle: RePEc:eee:apmaco:v:272:y:2016:i:p2:p:479-497
    DOI: 10.1016/j.amc.2015.08.042
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    Cited by:

    1. Minhajul, & Zeidan, D. & Raja Sekhar, T., 2018. "On the wave interactions in the drift-flux equations of two-phase flows," Applied Mathematics and Computation, Elsevier, vol. 327(C), pages 117-131.
    2. Busto, S. & Río-Martín, L. & Vázquez-Cendón, M.E. & Dumbser, M., 2021. "A semi-implicit hybrid finite volume/finite element scheme for all Mach number flows on staggered unstructured meshes," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    3. Busto, S. & Dumbser, M. & Río-Martín, L., 2023. "An Arbitrary-Lagrangian-Eulerian hybrid finite volume/finite element method on moving unstructured meshes for the Navier-Stokes equations," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    4. Boscheri, Walter & Tavelli, Maurizio, 2022. "High order semi-implicit schemes for viscous compressible flows in 3D," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    5. Saray Busto & Michael Dumbser & Laura Río-Martín, 2021. "Staggered Semi-Implicit Hybrid Finite Volume/Finite Element Schemes for Turbulent and Non-Newtonian Flows," Mathematics, MDPI, vol. 9(22), pages 1-38, November.

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