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. 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)
  2. 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)
  3. Bouchut, François; Lhébrard, Xavier: A multi well-balanced scheme for the shallow water MHD system with topography (2017)
  4. Castro, Manuel J.; Gallardo, José M.; Marquina, Antonio: New types of Jacobian-free approximate Riemann solvers for hyperbolic systems (2017)
  5. Castro, M.J.; Escalante, C.; Morales de Luna, T.: Modelling and simulation of non-hydrostatic shallow flows (2017)
  6. Tokareva, Svetlana; Toro, Eleuterio: A flux splitting method for the Baer-Nunziato equations of compressible two-phase flow (2017)
  7. Bürger, Raimund; Mulet, Pep; Rubio, Lihki: Polynomial viscosity methods for multispecies kinematic flow models (2016)
  8. Dumbser, Michael; Balsara, Dinshaw S.: A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems (2016)
  9. Castro Díaz, M.J.; Fernández-Nieto, E.D.; Narbona-Reina, G.; de la Asunción, M.: A second order PVM flux limiter method. Application to magnetohydrodynamics and shallow stratified flows (2014)
  10. Castro, Manuel J.; Gallardo, José M.; Marquina, Antonio: A class of incomplete Riemann solvers based on uniform rational approximations to the absolute value function (2014)
  11. Fernández-Nieto, E.D.; Koné, E.H.; Chacón Rebollo, T.: A multilayer method for the hydrostatic Navier-Stokes equations: a particular weak solution (2014)
  12. Morales de Luna, Tomás; Castro Díaz, Manuel J.; Parés, Carlos: Relation between PVM schemes and simple Riemann solvers (2014)
  13. Fernández-Nieto, E.D.; Koné, E.H.; Morales de Luna, T.; Bürger, R.: A multilayer shallow water system for polydisperse sedimentation (2013)
  14. Acary-Robert, C.; Fernández-Nieto, E.D.; Narbona-Reina, G.; Vigneaux, P.: A well-balanced finite volume-augmented Lagrangian method for an integrated Herschel-Bulkley model (2012)
  15. Castro Díaz, M.J.; Fernández-Nieto, E.: A class of computationally fast first order finite volume solvers: PVM methods (2012)