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In this paper, we present a rigorous numerical analysis for a bounded artificial viscosity model (τ = μδσa(δ∥∇su∥F )∇su) for the numerical simulation of turbulent flows. In practice, the commonly used Smagorinsky model (τ = (csδ)2∥∇su∥F ∇su) is overly dissipative and yields unphysical results. To date, several methods for "clipping" the Smagorinsky viscosity have proven useful in improving the physical characteristics of the simulated flow. However, such heuristic strategies strongly rely upon a priori knowledge of the flow regime. The bounded artificial viscosity model relies on a highly nonlinear, but monotone and smooth, semilinear elliptic form for the artificial viscosity. For this model, we have introduced a variational computational strategy, provided finite element error convergence estimates, and included several computational examples indicating its improvement on the overly diffusive Smagorinsky model. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a three-dimensional (3D), nonisothermal, multiphysics, two-phase steady state transport model and its efficient numerical methods are systematically studied for a full proton exchange membrane fuel cell (PEMFC) in the sense of efficiency and accuracy. The conservation equations of mass, momentum, species, charge and energy are fully addressed in view of nonisothermality and multiphase characteristics. In addition, from an accurate numerical discretization’s point of view, we present some new formulations for species equations by investigating the interactions among the species. In a framework of the combined finite element-upwind finite volume method, some efficient numerical methods are developed in terms of Kirchhoff transformation for the sake of a fast and convergent numerical simulation. The 3D simulations demonstrate that the convergent solutions can be attained within 80 nonlinear iterations, in contrast to the oscillating and nonconvergent iterations conducted by commercial flow solvers or in-house code with standard finite element/volume methods. Numerical convergence tests are carried out to verify the efficiency and accuracy of our numerical algorithms and techniques. [Copyright &y& Elsevier]