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. Garres-Díaz, J.; Fernández-Nieto, E. D.; Mangeney, A.; Morales de Luna, T.: A weakly non-hydrostatic shallow model for dry granular flows (2021)
  2. Pimentel-García, Ernesto; Parés, Carlos; Castro, Manuel J.; Koellermeier, Julian: On the efficient implementation of PVM methods and simple Riemann solvers. Application to the Roe method for large hyperbolic systems (2021)
  3. Bürger, Raimund; Fernández-Nieto, Enrique D.; Osores, Víctor: A multilayer shallow water approach for polydisperse sedimentation with sediment compressibility and mixture viscosity (2020)
  4. Castro, Manuel J.; Parés, Carlos: Well-balanced high-order finite volume methods for systems of balance laws (2020)
  5. Delgado-Sánchez, J. M.; Bouchut, Francois; Fernández-Nieto, E. D.; Mangeney, A.; Narbona-Reina, G.: A two-layer shallow flow model with two axes of integration, well-balanced discretization and application to submarine avalanches (2020)
  6. Escalante, C.; Morales de Luna, Tomás: A general non-hydrostatic hyperbolic formulation for Boussinesq dispersive shallow flows and its numerical approximation (2020)
  7. Ferreiro-Ferreiro, A. M.; García-Rodríguez, J. A.; López-Salas, J. G.; Escalante, C.; Castro, M. J.: Global optimization for data assimilation in landslide tsunami models (2020)
  8. Toro, E. F.; Saggiorato, B.; Tokareva, S.; Hidalgo, A.: Low-dissipation centred schemes for hyperbolic equations in conservative and non-conservative form (2020)
  9. Uilhoorn, F. E.: Numerical issues in gas flow dynamics with hydraulic shocks using high order finite volume WENO schemes (2020)
  10. Bürger, Raimund; Fernández-Nieto, Enrique D.; Osores, Víctor: A dynamic multilayer shallow water model for polydisperse sedimentation (2019)
  11. Díaz, Manuel Jesús Castro; Kurganov, Alexander; de Luna, Tomás Morales: Path-conservative central-upwind schemes for nonconservative hyperbolic systems (2019)
  12. Escalante, C.; Dumbser, M.; Castro, M. J.: An efficient hyperbolic relaxation system for dispersive non-hydrostatic water waves and its solution with high order discontinuous Galerkin schemes (2019)
  13. 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)
  14. Gallardo, José M.; Schneider, Kleiton A.; Castro, Manuel J.: On a class of two-dimensional incomplete Riemann solvers (2019)
  15. 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)
  16. Castro, Manuel J.; Ortega, Sergio; Parés, Carlos: Reprint of: “Well-balanced methods for the shallow water equations in spherical coordinates” (2018)
  17. 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)
  18. Escalante, C.; Morales de Luna, T.; Castro, M. J.: Non-hydrostatic pressure shallow flows: GPU implementation using finite volume and finite difference scheme (2018)
  19. 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)
  20. Gaburro, Elena; Castro, Manuel J.; Dumbser, Michael: A well balanced diffuse interface method for complex nonhydrostatic free surface flows (2018)

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