Method of Manufactured Solutions to Verify Three-Dimensional Least-Squares Finite Element Model of Generalized Newtonian Fluids

Abstract

A mixed least-squares finite element model (LSFEM) with spectral/hp approximations was developed for three-dimensional (3D) nonisothermal flows of a generalized Newtonian fluid, which obeys the power-law constitutive model. The finite element model consists of velocity, pressure, viscous stress, temperature, and heat flux as the field variables. A least-squares formulation provides a variational framework for the Navier–Stokes equations and does not require compatibility of the approximation spaces for field variables. Also, using spectral/hp elements in conjunction with the least-squares formulation, various forms of locking can be avoided, which often appear in low-order least-squares finite element models for incompressible viscous flows; thus, accurate results are obtained with exponential convergence in least-squares functionals. The method of manufactured solutions (MMS) is used to verify the present code.