  A universal particle velocity based algorithm for simulating hydraulic
fractures, previously proposed for Newtonian fluids, is extended to the class
of shear-thinning fluids. The scheme is not limited to any particular
elasticity operator or crack propagation regime. The computations are based on
two dependent variables: the crack opening and the reduced particle velocity.
The application of the latter facilitates utilization of the local condition of
Stefan type (speed equation) to trace the fracture front. The condition is
given in a general explicit form which relates the crack propagation speed (and
the crack length) to the solution tip asymptotics. The utilization of a modular
structure, and the adaptive character of its basic blocks, result in a flexible
numerical scheme. The computational accuracy of the proposed algorithm is
validated against a number of analytical benchmark solutions.
