We present a class of fast first-order finite volume solvers, called PVM (polynomial viscosity matrix), for balance laws or, more generally, for nonconservative hyperbolic systems. They are defined in terms of viscosity matrices computed by a suitable polynomial evaluation of a Roe matrix. These methods have the advantage that they only need some information about the eigenvalues of the system to be defined, and no spectral decomposition of a Roe matrix is needed

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  1. Castro, Manuel J.; Parés, Carlos: Well-balanced high-order finite volume methods for systems of balance laws (2020)
  2. Escalante, C.; Morales de Luna, Tomás: A general non-hydrostatic hyperbolic formulation for Boussinesq dispersive shallow flows and its numerical approximation (2020)
  3. Toro, E. F.; Saggiorato, B.; Tokareva, S.; Hidalgo, A.: Low-dissipation centred schemes for hyperbolic equations in conservative and non-conservative form (2020)
  4. Bürger, Raimund; Fernández-Nieto, Enrique D.; Osores, Víctor: A dynamic multilayer shallow water model for polydisperse sedimentation (2019)
  5. Díaz, Manuel Jesús Castro; Kurganov, Alexander; de Luna, Tomás Morales: Path-conservative central-upwind schemes for nonconservative hyperbolic systems (2019)
  6. Escalante, C.; Fernández-Nieto, E. D.; Morales de Luna, T.; Castro, M. J.: An efficient two-layer non-hydrostatic approach for dispersive water waves (2019)
  7. Balsara, Dinshaw S.; Li, Jiequan; Montecinos, Gino I.: An efficient, second order accurate, universal generalized Riemann problem solver based on the HLLI Riemann solver (2018)
  8. Castro, Manuel J.; Ortega, Sergio; Parés, Carlos: Reprint of: “Well-balanced methods for the shallow water equations in spherical coordinates” (2018)
  9. De Lorenzo, M.; Pelanti, M.; Lafon, Ph.: HLLC-type and path-conservative schemes for a single-velocity six-equation two-phase flow model: a comparative study (2018)
  10. Escalante, C.; Morales de Luna, T.; Castro, M. J.: Non-hydrostatic pressure shallow flows: GPU implementation using finite volume and finite difference scheme (2018)
  11. Fernández-Nieto, E. D.; Garres-Díaz, J.; Mangeney, A.; Narbona-Reina, G.: 2D granular flows with the (\mu(I)) rheology and side walls friction: a well-balanced multilayer discretization (2018)
  12. Gaburro, Elena; Castro, Manuel J.; Dumbser, Michael: A well balanced diffuse interface method for complex nonhydrostatic free surface flows (2018)
  13. Kurganov, Alexander: Finite-volume schemes for shallow-water equations (2018)
  14. Balsara, Dinshaw S.; Nkonga, Boniface: Multidimensional Riemann problem with self-similar internal structure. Part III: A multidimensional analogue of the HLLI Riemann solver for conservative hyperbolic systems (2017)
  15. Bouchut, François; Lhébrard, Xavier: A multi well-balanced scheme for the shallow water MHD system with topography (2017)
  16. Castro, Manuel J.; Gallardo, José M.; Marquina, Antonio: New types of Jacobian-free approximate Riemann solvers for hyperbolic systems (2017)
  17. Castro, Manuel J.; Ortega, Sergio; Parés, Carlos: Well-balanced methods for the shallow water equations in spherical coordinates (2017)
  18. Castro, M. J.; Escalante, C.; Morales de Luna, T.: Modelling and simulation of non-hydrostatic shallow flows (2017)
  19. Tokareva, Svetlana; Toro, Eleuterio: A flux splitting method for the Baer-Nunziato equations of compressible two-phase flow (2017)
  20. Bürger, Raimund; Mulet, Pep; Rubio, Lihki: Polynomial viscosity methods for multispecies kinematic flow models (2016)

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