  A method for modelling non-Newtonian fluids (dilatants and pseudoplastics) by
a power law under the Godunov-Peshkov-Romenski model is presented, along with a
new numerical scheme for solving this system. The scheme is also modified to
solve the corresponding system for power-law elastoplastic solids.
  The scheme is based on a temporal operator splitting, with the homogeneous
system solved using a finite volume method based on a WENO reconstruction, and
the temporal ODEs solved using an analytical approximate solution. The method
is found to perform favorably against problems with known exact solutions, and
numerical solutions published in the open literature. It is simple to
implement, and to the best of the authors' knowledge it is currently the only
method for solving this modified version of the GPR model.
