Numerics for Hyperbolic Conservation Laws with Help from the Physical   Entropy
  Stable numerical simulations for a hyperbolic system of conservation laws of relaxation type but not in divergence form are obtained by incorporating the physical entropy into the simulations. The entropy balance is utilized as an additional equation to eliminate the numerically critical terms with simple substitutions. The method has potential for a wider applicability than the particular example presented here. 
Carl Philipp Zinner and Hans Christian \"Ottinger
math.NA physics.comp-ph physics.flu-dyn