An improved unsteady, unstructured, artificial compressibility, finite volume scheme for viscous incompressible flows: Part II. Application

Malan, Arnaud G.; Lewis, R. W.; Nithiarasu, Perumal

doi:10.1002/nme.443

Cited by 53 publications

(50 citation statements)

References 18 publications

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“…They applied the method for problems including lid-driven cavity, backward facing step, buoyancy-driven cavity flow, and Von Karmann vortex street [48]. Nevertheless, the numerical experimentation performed in this study showed that by employing the MPM in the viscous flows over the NACA-hydrofoils, the convergence occurs at low level convergence criteria.…”

Section: Power-law Preconditionermentioning

confidence: 80%

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An improved progressive preconditioning method for steady non‐cavitating and sheet‐cavitating flows

Esfahanian

Akbarzadeh

Hejranfar

2010

Numerical Methods in Fluids

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SUMMARYAn improved progressive preconditioning method for analyzing steady inviscid and laminar flows around fully wetted and sheet-cavitating hydrofoils is presented. The preconditioning matrix is adapted automatically from the pressure and/or velocity flow-field by a power-law relation. The cavitating calculations are based on a single fluid approach. In this approach, the liquid/vapour mixture is treated as a homogeneous fluid whose density is controlled by a barotropic state law. This physical model is integrated with a numerical resolution derived from the cell-centered Jameson's finite volume algorithm. The stabilization is achieved via the second-and fourth-order artificial dissipation scheme. Explicit four-step Runge-Kutta time integration is applied to achieve the steady-state condition. Results presented in the paper focus on the pressure distribution on hydrofoils wall, velocity profiles, lift and drag forces, length of sheet cavitation, and effect of the power-law preconditioning method on convergence speed. The results show satisfactory agreement with numerical and experimental works of others. The scheme has a progressive effect on the convergence speed. The results indicate that using the power-law preconditioner improves the convergence rate, significantly.

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Section: Power-law Preconditionermentioning

confidence: 80%

“…Actually, the introduced preconditioning scheme is the extended and modified one which was originally initiated by Malan [2] (Malan's PM). It is worth to mention that Malan applied his method for problems including lid-driven cavity, backward facing step, buoyancy-driven cavity flow, and Von Karmann vortex street [48].…”

Section: Introductionmentioning

confidence: 99%

An improved progressive preconditioning method for steady non‐cavitating and sheet‐cavitating flows

Esfahanian

Akbarzadeh

Hejranfar

2010

Numerical Methods in Fluids

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“…where u i are the Cartesian components of the velocity vector, is the fluid density, p represents the pressure and is an artificial compressibility parameter [36][37][38][39][40][41][42][43][44]. The deviatoric stress components ij are related to the velocity gradients by…”

Section: The Navier-stokes Equations For Incompressible Flowmentioning

confidence: 99%

Application of a locally conservative Galerkin (LCG) method for modelling blood flow through a patient‐specific carotid bifurcation

Bevan

Nithiarasu

Loon

et al. 2010

Numerical Methods in Fluids

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SUMMARYIn the present work, blood flow through a patient-specific carotid bifurcation is thoroughly analysed. A locally conservative Galerkin spatial discretization is applied along with an artificial compressibility and characteristic-based split scheme to solve the 3D incompressible Navier-Stokes equations. Boundary layer meshes are introduced to accurately resolve high near-wall velocity gradients inside a patient-specific carotid bifurcation. A total of six haemodynamic wall parameters have been brought together to analyse the regions of possible atherogenesis within the domain. The results show that wall shear stress (WSS) is high (6-15 Pa) near the apex, along with a small region where WSS exceeded 20 Pa. This peak WSS region is close to the inner wall of the external carotid artery (ECA). It is also clear from the results that low WSS occurred in the common carotid artery (CCA). High oscillatory shear occurred in the CCA distal to a local narrowing of the internal carotid artery and along the outer wall, indicating a potential region of atherogenesis. The highest values of wall shear stress angle deviation and wall shear stress angle gradient occur at the apex. The wall shear stress temporal gradient reached 4000 Pa/s near the apex, closer to the ECA. Wall shear stress spatial gradient distribution corresponded with the WSS distribution, with a maximum occurring at the apex.

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“…The system of equations is made up of the momentum equations and the incompressibility relation, and it is well known that the main difficulties in its solution reside in the approximation of the convective term and in the calculation of the pressure. A large amount of numerical methods have been developed particularly in the framework of finite elements (FE) (Baker, Dougalis, & Karakashian, 1982;Choi, Choi, & Yoo, 1997;Codina & Soto, 2004;Plana Fattori, Chantoiseau, Doursat, & Flick, 2013;Sun, Zhang, & Ren, 2012), of cell-centred finite volumes (Deponti, Pennati, & De Biase, 2006;Feraudi & Pennati, 1997;Kim & Moin, 1985;Pai, Prakash, & Patnaik, 2013) or cell-vertex finite volumes (Hookey & Baliga, 1998;Malan, Lewis, & Nithiarasu, 2002;Tritthart & Gutknecht, 2007;Vrahliotis, Pappou, & Tsangaris, 2012) and finite differences (Ali, Fieldhouse, & Talbot, 2011;Kumar, Dass, & Dewan, 2010;Shih & Tan, 1989). In the finite difference (FD) and finite volume (FV) *Corresponding author.…”

Section: Introductionmentioning

confidence: 99%

A cost-effective FE method for 2D Navier–Stokes equations

Jotsa

Pennati

2015

Engineering Applications of Computational Fluid Mechanics

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A cost-effective approach to the solution of 2D Navier-Stokes equations for incompressible fluid flow problems is presented. The aim is to reach a good compromise between numerical properties and computational efficiency. In order to achieve the set goal, the nonlinear convective terms are approximated by means of characteristics and spatial approximations of equal order are performed by polynomials of degree two. In this way, the computational kernels are reduced to elliptic ones for which solution very efficient techniques are available. The time-advancing is afforded by a fractional step method combined with a stabilization technique suitably simplified, so that the inf-sup condition is easily overcome. The algebraic systems generated by the new technique are solved by an iterative solver (Bi-CGSTAB), preconditioned by means of a suitable Schwarz additive scalable preconditioner. The properties of the new method have been confirmed from the comparison among the results obtained by it, and those obtained from other methods in the solution of some well known test problems. The obtained results, both in terms of accuracy and computational efficiency, make realistic the possibility to extend the method to 3D problems and to develop a multidomain approach.

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An improved unsteady, unstructured, artificial compressibility, finite volume scheme for viscous incompressible flows: Part II. Application

Cited by 53 publications

References 18 publications

An improved progressive preconditioning method for steady non‐cavitating and sheet‐cavitating flows

An improved progressive preconditioning method for steady non‐cavitating and sheet‐cavitating flows

Application of a locally conservative Galerkin (LCG) method for modelling blood flow through a patient‐specific carotid bifurcation

A cost-effective FE method for 2D Navier–Stokes equations

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