3.2.8 Entropy production by artificial viscosity

A possibly way to prevent the violation of the entropy condition (172) is to produce entropy with an extra (artifical) diffusion term added to the CIR flux (185) according to

 (187)
However, now the parameter has to be tuned to be large enough to give the correct weak solution while not smearing it more than necessary.

The viscosity parameter could be replaced e.g. by the function

 (188)
to confine the extra viscosity to regions where the gradient is really large.