Impact of Artificial Compressibility on the Numerical Solution of Incompressible Nanofluid Flow

The numerical solution of compressible flows has become more prevalent than that of incompressible flows.With the help of the artificial compressibility approach,incompressible flows can be solved numerically using the same methods as compressible ones.The artificial compressibility scheme is thus widely used to numerically solve incompressible Navier-Stokes equations.Any numerical method highly depends on its accuracy and speed of convergence.Although the artificial compressibility approach is utilized in several numerical simulations,the effect of the compressibility factor on the accuracy of results and convergence speed has not been investigated for nanofluid flows in previous studies.Therefore,this paper assesses the effect of this factor on the convergence speed and accuracy of results for various types of thermo-flow.To improve the stability and convergence speed of time discretizations,the fifth-order Runge-Kutta method is applied.A computer program has been written in FORTRAN to solve the discretized equations in different Reynolds and Grashof numbers for various grids.The results demonstrate that the artificial compressibility factor has a noticeable effect on the accuracy and convergence rate of the simulation.The optimum artificial compressibility is found to be between 1 and 5.These findings can be utilized to enhance the performance of commercial numerical simulation tools,including ANSYS and COMSOL.

UNSTEADY/STEADY NUMERICAL SIMULATION OF THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON ARTIFICIAL COMPRESSIBILITY

A mixed algorithm of central and upwind difference scheme for the solution of steady/unsteady incompressible Navier-Stokes equations is presented. The algorithm is based on the method of artificial compressibility and uses a third-order flux-difference splitting technique for the convective terms and the second-order central difference for the viscous terms. The numerical flux of semi-discrete equations is computed by using the Roe approximation. Time accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The algebraic turbulence model of Baldwin-Lomax is ulsed in this work. As examples, the solutions of flow through two dimensional flat, airfoil, prolate spheroid and cerebral aneurysm are computed and the results are compared with experimental data. The results show that the coefficient of pressure and skin friction are agreement with experimental data, the largest discrepancy occur in the separation region where the lagebraic turbulence model of Baldwin-Lomax could not exactly predict the flow.

OBLC Domain Decomposition for Artificial Compressible Equation

This paper is a continuation of the domain decomposition method according to thephysics scale proposed in [1] and [2]. Starting from systems of ordinary differentialequattons, a solution is decomposed into an outer solution (0) and its boundary layercorrections (BLC) mainly on the fixed boundary. For efficient numerical solution,different equations, different numerical methods and different grids can be suitablychosen for the different scales. This paper also gives the characteristic nature and well-posed boundary condition about artificial compressible equations. Numericalexperiments show that the computational method and the couple process presented inthe paper are effective.

Numerical analysis of hemodynamic parameters in stenosed arteries under pulsatile flow conditions

This research studies the changes in flow patterns and hemodynamic parameters of diverse shapes and sizes of stenosis.Six different shapes and sizes of stenosis are constructed to investigate the variations in hemodynamics as the morphology changes.Changes in shape(trapezoidal and bell-shaped)and sizes of stenosis change the stresses on the walls and their flow patterns.TAWSS and OSI results specify that trapezoidal stenosis exerts greater stress than bell-shaped stenosis.Also,as the length of the trapezoidal stenosis increases,the TAWSS increases,whereas the trend is the opposite for bell-shaped stenosis.Later,this paper also studies different degrees of stenosis extracted from real images.Changes in velocity flow patterns,wall shear stress(WSS),Time-averaged wall shear stress(TAWSS)and Oscillatory shear index(OSI)have been studied for these images.Results illustrate that the peak velocity rises drastically as the stenosis percentage increases.Negative velocity is seen close to the artery's walls,indicating flow separation.This flow separation region is seen throughout the cycle except in the accelerating flow region.An increase in stenosis also increases WSS and TAWSS drastically.Negative WSS is seen downstream of stenosis,indicating flow recirculation.Such negative WSS in the blood vessels also promotes endothelial dysfunction.OSI values greater than 0.2 are seen near the stenosis region,indicating atherosclerosis growth.Regions of high OSI and low TAWSS are also identified,indicating probable regions of plaque development.

A Third-Order Upwind Compact Scheme on Curvilinear Meshes for the Incompressible Navier-Stokes Equations

This paper presents a new version of the upwind compact finite difference scheme for solving the incompressible Navier-Stokes equations in generalized curvilinear coordinates.The artificial compressibility approach is used,which transforms the elliptic-parabolic equations into the hyperbolic-parabolic ones so that flux difference splitting can be applied.The convective terms are approximated by a third-order upwind compact scheme implemented with flux difference splitting,and the viscous terms are approximated by a fourth-order central compact scheme.The solution algorithm used is the Beam-Warming approximate factorization scheme.Numerical solutions to benchmark problems of the steady plane Couette-Poiseuille flow,the liddriven cavity flow,and the constricting channel flow with varying geometry are presented.The computed results are found in good agreement with established analytical and numerical results.The third-order accuracy of the scheme is verified on uniform rectangular meshes.

The Locally Conservative Galerkin (LCG) Method — a Discontinuous Methodology Applied to a Continuous Framework

This paper presents a comprehensive overview of the element-wise locally conservative Galerkin(LCG)method.The LCG method was developed to find a method that had the advantages of the discontinuous Galerkin methods,without the large computational and memory requirements.The initial application of the method is discussed,to the simple scalar transient convection-diffusion equation,along with its extension to the Navier-Stokes equations utilising the Characteristic Based Split(CBS)scheme.The element-by-element solution approach removes the standard finite element assembly necessity,with an face flux providing continuity between these elemental subdomains.This face flux provides explicit local conservation and can be determined via a simple small post-processing calculation.The LCG method obtains a unique solution from the elemental contributions through the use of simple averaging.It is shown within this paper that the LCG method provides equivalent solutions to the continuous(global)Galerkin method for both steady state and transient solutions.Several numerical examples are provided to demonstrate the abilities of the LCG method.

A High-Order Direct Discontinuous Galerkin Method for Variable Density Incompressible Flows

In this work,we develop a novel high-order discontinuous Galerkin(DG)method for solving the incompressible Navier-Stokes equations with variable density.The incompressibility constraint at cell interfaces is relaxed by an artificial compressibility term.Then,since the hyperbolic nature of the governing equations is recovered,the simple and robust Harten-Lax-van Leer(HLL)flux is applied to discrete the inviscid term of the variable density incompressible Navier-Stokes equations.The viscous term is discretized by the direct DG(DDG)method,the construction of which was initially inspired by the weak solution of a scalar diffusion equation.In addition,in order to eliminate the spurious oscillations around sharp density gradients,a local slope limiting operator is also applied during the highly stratified flow simulations.The convergence property and performance of the present high-order DDG method are well demonstrated by several benchmark and challenging numerical test cases.Due to its advantages of simplicity and robustness in implementation,the present method offers an effective approach for simulating the variable density incompressible flows.