A Two-Dimensional Version of the Godunov Scheme for Scalar Balance Laws

@article{Gosse2014ATV,
  title={A Two-Dimensional Version of the Godunov Scheme for Scalar Balance Laws},
  author={Laurent Gosse},
  journal={SIAM J. Numerical Analysis},
  year={2014},
  volume={52},
  pages={626-652}
}
A Godunov scheme is derived for two-dimensional scalar conservation laws without or with source terms following ideas originally proposed by Boukadida and LeRoux [6] in the context of a staggered Lax-Friedrichs scheme. In both situations, the numerical fluxes are obtained at each interface of a uniform Cartesian computational grid just by means of the “external waves” involved in the entropy solution of the elementary 2d Riemann problems; in particular, all the wave-interaction phenomena is… CONTINUE READING