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, E. Guerrero; Díaz, M. J. Castro; Dumbser, M.; de Luna, T. Morales: An arbitrary high order well-balanced ADER-DG numerical scheme for the multilayer shallow-water model with variable density (2022)
  2. Koellermeier, Julian; Pimentel-García, Ernesto: Steady states and well-balanced schemes for shallow water moment equations with topography (2022)
  3. Escalante, C.; Castro, M. J.; Semplice, M.: Very high order well-balanced schemes for non-prismatic one-dimensional channels with arbitrary shape (2021)
  4. Garres-Díaz, J.; Fernández-Nieto, E. D.; Mangeney, A.; Morales de Luna, T.: A weakly non-hydrostatic shallow model for dry granular flows (2021)
  5. Garres-Díaz, José; Díaz, Manuel J. Castro; Koellermeier, Julian; de Luna, Tomás Morales: Shallow water moment models for bedload transport problems (2021)
  6. LeFloch, Philippe G.; Parés, Carlos; Pimentel-García, Ernesto: A class of well-balanced algorithms for relativistic fluids on a Schwarzschild background (2021)
  7. 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)
  8. Sánchez, Cipriano Escalante; Fernández-Nieto, Enrique D.; Morales de Luna, Tomás; Penel, Yohan; Sainte-Marie, Jacques: Numerical simulations of a dispersive model approximating free-surface Euler equations (2021)
  9. Schneider, Kleiton A.; Gallardo, José M.; Balsara, Dinshaw S.; Nkonga, Boniface; Parés, Carlos: Multidimensional approximate Riemann solvers for hyperbolic nonconservative systems. Applications to shallow water systems (2021)
  10. Bürger, Raimund; Fernández-Nieto, Enrique D.; Osores, Víctor: A multilayer shallow water approach for polydisperse sedimentation with sediment compressibility and mixture viscosity (2020)
  11. Castro, Manuel J.; Parés, Carlos: Well-balanced high-order finite volume methods for systems of balance laws (2020)
  12. 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)
  13. Escalante, C.; Morales de Luna, Tomás: A general non-hydrostatic hyperbolic formulation for Boussinesq dispersive shallow flows and its numerical approximation (2020)
  14. 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)
  15. Toro, E. F.; Saggiorato, B.; Tokareva, S.; Hidalgo, A.: Low-dissipation centred schemes for hyperbolic equations in conservative and non-conservative form (2020)
  16. Uilhoorn, F. E.: Numerical issues in gas flow dynamics with hydraulic shocks using high order finite volume WENO schemes (2020)
  17. Bürger, Raimund; Fernández-Nieto, Enrique D.; Osores, Víctor: A dynamic multilayer shallow water model for polydisperse sedimentation (2019)
  18. Díaz, Manuel Jesús Castro; Kurganov, Alexander; de Luna, Tomás Morales: Path-conservative central-upwind schemes for nonconservative hyperbolic systems (2019)
  19. 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)
  20. 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)

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