Optimal linearization state for local characteristic decomposition

Determine the best representative average interface state, and hence the best linearization option, for the local characteristic decomposition used in high-order numerical methods for hyperbolic systems of conservation laws.

Background

Local characteristic decomposition for systems of hyperbolic conservation laws requires linearizing the flux Jacobian at a representative average state associated with a cell interface. In numerical implementations, this state is commonly constructed from neighboring solution values using arithmetic or Roe-type averages.

The paper introduces an entropy-based local characteristic decomposition as an alternative that selects an interface state by locally minimizing entropy among candidate states. However, the paper does not establish that this or any other averaging procedure is optimal; the general question of which linearization option is best remains unresolved.