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In current pagination the flow problems involving shear rate dependent nonlinear viscosity have been treated successfully in the sense of space discretization and solvers. The stable finite element pair Q 2 / P 1 disc is employed to approximate the velocity and pressure spaces independently. Discretized form of non-linear expressions is linearized by implementing Newton’s procedure and the resulting systems are solved using a geometric multigrid approach. The flow generated by way of driven cavity and by an obstacle are very important benchmarks of computational fluid dynamics. In current pagination shear rate reliant viscosity model renowned as Carreau Yasuda fluid is capitalized. The obtained results are demonstrated and analyzed with the help of velocity and viscosity plots. In addition, we have produced new reference data for kinetic energy (K.E) for driven cavity problem and drag and lift coefficients for circular obstacle problem. The obtained results for driven cavity problem reveal the fact that K.E is an increasing function of the relaxation parameter ( λ ) and power law exponent (n) whereas a decreasing function of the model parameter ( a ) . For the case of flow around obstacle the drag coefficient ( C D ) and the lift coefficient ( C L ) show strong dependence on ( λ ) and ( n ) , however a weak dependence on the parameter ( a ) .

In this article we consider a smooth channel with infinite length. A circular cylinder is placed in the channel as an obstacle. A fluid satisfying Newton’s law of viscosity is taken in the channel with two different classes of velocity profiles at the inlet namely, a linear (constant) velocity profile and a parabolic profile. The mathematical model is structured by using the fundamental laws involved in the field of fluid rheology. Since the flow-describing differential equations are nonlinear in nature, a computational scheme is executed to report the primitive flow field quantities that is the pressure and the velocity. The numerical method used in this case is the finite-element method. The obtained outcomes are given by way of graphical trends. For a clear insight both the contour plots and line graphs are added. Further, the benchmark quantities namely, the drag and the lift coefficients are evaluated around the outer surface of the obstacle through the line integration. For accuracy the numerical data subject to both the drag and the lift coefficients is recorded up to nine different refinement mesh levels. Finally, the findings are concluded with the potential remark that the flow in a channel (having no-slip condition at both the lower and upper walls) with the parabolic velocity profile initiated at the inlet is the more realistic approach as compared to the linear (constant) profile being considered at the inlet.

In this paper, numerical simulations are performed in a single and double lid driven square cavity to study the flow of a Bingham viscoplastic fluid. The governing equations are discretized with the help of finite element method in space and the nonconforming Stokes elementQ~1/Q0is utilized which gives 2nd-order accuracy for velocity and 1st-order accuracy for pressure. The discretized systems of nonlinear equations are treated by using the Newton method and the inner linear subproablems are solved by the direct solver UMFPACK. A qualitative comparison is done with the results reported in the literature. In addition to these comparisons, some new reference data for the kinetic energy is generated. All these implementations are done in the open source software package FEATFLOW which is a general purpose finite element based solver package for solving partial differential equations.

This paper presents the stationary Bingham fluid flow simulations past a circular cylinder placed in a channel. The governing equations of motion are discretized using the mixed finite element method. The biquadratic element Q2 is used to approximate the velocity space and Pdisc for the pressure space. This LBB-stable finite element pair $$Q_{2} /P_{1}^{\text{disc}}$$ leads to an accuracy of third and second order in L2-norm for velocity and pressure approximations, respectively. The discrete version of the nonlinear system is linearized by the Newton’s method, and the linear subproblems as an inner loop are coped with UMFPACK solver. Code validation and grid independence study is also presented to confirm the reliability of the results. Simulations are carried out for various values of dimensionless Bingham number Bn, and its impact is investigated with great detail by demonstrating the velocity, viscosity and pressure contours. The benchmark quantities like drag coefficient (CD) and lift coefficient (CL) are also discussed graphically and quantitatively. Moreover, two different locations of the circular cylinder are considered for the analysis of hydrodynamic forces.

In this paper, we implement the non-conforming finite elements for the simulation of two dimensional incompressible Newtonian fluid flows. The classical driven cavity benchmark problem is simulated on a very fine uniform grid. In order to discretize the governing partial differential equations (PDEs) we employ the rotated bilinear Q ˜ 1 element for velocity and piecewise constant Q 0 element for the pressure on the general quadrilateral meshes. In L 2 -norm this pair is 2 nd order accurate for velocity and provides 1st order accuracy for pressure approximations. For the solution of non-linear systems arising from the discretization, Newton’s method is used as an outer nonlinear iteration and for the inner linear sub problems, the direct solver UMFPACK is utilized. The results have been compared with the reference data present in the literature and a good agreement is found.

This paper aims to present complete series solution of non-similarity boundary-layer flow of an incompressible viscous fluid over a porous wedge. The corresponding nonlinear partial differential equations are solved analytically by means of the homotopy analysis method (HAM). An auxiliary parameter is introduced to ensure the convergence of solution series. As a result, series solutions valid for all physical parameters in the whole domain are given. Then, the effects of physical parameters γ and Prandtl number Pr on the local Nusselt number and momentum thickness are investigated. To the best of our knowledge, it is the first time that the series solutions of this kind of non-similarity boundary-layer flows are reported.

The unsteady non-similarity boundary-layer flows caused by an impulsively stretching flat sheet have been investigated. The partial differential equations governing the flows have been solved analytically by means of an analytic technique for strongly non-linear problems, namely the homotopy analysis method (HAM). This analytic approach gives us the convergent series solution uniformly valid for all dimensionless time in the whole spatial region 0 ≤ x ∞ and 0 ≤ y ∞ . To the best of our knowledge, such a kind of series solution has never been obtained. The skin friction coefficient and the boundary-layer thickness are also analyzed for different dimensionless time τ .

The non-similarity solution for natural convection from a permeable isothermal vertical wall is considered. The governing boundary-layer equations for non-similarity flow and temperature fields are solved using the homotopy analysis method. The homotopy-Pade technique is applied to accelerate the convergence of the homotopy-series solution. The influence of physical parameters on the non-similarity flows is investigated in detail. Different from the previous analytic results, the homotopy-series solutions are convergent and valid for all physical parameters in the whole domain 0 ⩽ x < ∞ and 0 ⩽ y < ∞.