A Wave Propagation Method for Conservation Laws and Balance Laws with Spatially Varying Flux Functions

@article{Bale2003AWP,
  title={A Wave Propagation Method for Conservation Laws and Balance Laws with Spatially Varying Flux Functions},
  author={Derek S. Bale and Randall J. LeVeque and Sorin Mitran and James A. Rossmanith},
  journal={SIAM J. Scientific Computing},
  year={2003},
  volume={24},
  pages={955-978}
}
We study a general approach to solving conservation laws of the form qt+f(q, x)x = 0, where the flux function f(q, x) has explicit spatial variation. Finite-volume methods are used in which the flux is discretized spatially, giving a function fi(q) over the ith grid cell and leading to a generalized Riemann problem between neighboring grid cells. A high-resolution wave-propagation algorithm is defined in which waves are based directly on a decomposition of flux differences fi(Qi)− fi−1(Qi−1… CONTINUE READING

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