A development of a GSM-CFD solver for non-Newtonian flows

- An incompressible GSM-CFD solver is firstly developed for non-Newtonian fluids.
- The convective and viscous flux in the Navier-Stokes equations are approximated by the gradient smoothing operations.
- The proposed solver is validated by a benchmark problem of the power-law fluids past a circular cylinder.
- The critical Reynolds number decreases with an increasing power index.

An incompressible GSM-CFD solver based on the gradient smoothing method (GSM) is developed for solving non-Newtonian fluids in this paper. Node-based and edge-based smoothing domains are constructed to approximate the first- and second-order derivatives in the strong form Navier-Stokes equations. The non-Newtonian constitute law is implemented by using a generalized Newtonian fluid model with viscosity obeying the power-law. The widely used benchmark problem of flow past a circular cylinder is analyzed to validate the proposed solver by comparing it with numerical and experimental results available in the literature. The detailed comparison study on the results of wake length, separation angle and the drag coefficient demonstrates the accuracy and robustness of the present GSM-CFD solver. Our study also revealed the strong dependence of the flow behavior on the power index.