We provide numerical simulations of an incompressible pressure-thickening andshear-thinning lubricant flowing in a plane slider bearing. We study theinfluence of several parameters, namely the ratio of the characteristic lengths$\varepsilon>0$ (with $\varepsilon\searrow0$ representing the Reynoldslubrication approximation); the coefficient of the exponentialpressure--viscosity relation $\alpha^*\geq0$; the parameter $G^*\geq0$ relatedto the Carreau--Yasuda shear-thinning model and the modified Reynolds number$\mathrm{Re}_\varepsilon\geq0$. The finite element approximations to the steadyisothermal flows are computed without resorting to the lubricationapproximation. We obtain the numerical solutions as long as the variation ofthe viscous stress $\mathbf{S}=2\eta(p,\mathrm{tr}\mathbf{D}^2)\mathbf{D}$ withthe pressure is limited, say $|\partial\mathbf{S}/\partial p|\leq1$. We showconclusively that the existing practice of avoiding the numerical difficultiesby cutting the viscosity off for large pressures leads to results that dependsorely on the artificial cut-off parameter. We observe that the piezoviscousrheology generates pressure differences across the fluid film.
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