A chebyshev collocation spectral method for numerical simulation of incompressible flow problems

Martinez, Johnny de Jesús; Esperança, Paulo T. T.

doi:10.1590/s1678-58782007000300013

Cited by 16 publications

(8 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For laminar boundary layer over a flat plate with suction or blowing, this quantity is not known explicitly, but it is obtained numerically from the nonlinear ordinary differential Blasius equation (11) subject to the boundary conditions (14) where is the similarity coordinate and f the non dimensional stream function given by Skan-Falkner transformation:…”

Section: Mean Flow Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Study of the Effect of Parietal Suction and Blowing on the Stability of Laminar External Flow

Laouer¹,

Mezaache²,

Laouar³

2016

IJHT

View full text Add to dashboard Cite

Stability and transition problems of two dimensional laminar external flow over a flat plate with wall suction and blowing are studied numerically using the temporal linear stability theory. The flow is assumed similar two-dimensional laminar boundary-layer. The mean velocity profiles are obtained numerically for the case of suction or blowing. The stability equation is given in a general form which can be applied to Chebyshev domain and in boundary layer domain and solved numerically by the Chebyshev collocation spectral method. The neutral stability curves and the critical Reynolds numbers are presented.

show abstract

Section: Mean Flow Equationsmentioning

confidence: 99%

“…The superior performance of the Chebyshev tau method compared to existing finitedifference and spectral schemes led to its application to a diverse range of stability problems [11]. Dongarra et al [12] and Melenk et al [13] consider a general mathematical framework spectral methods for hydrodynamic stability problems.…”

Section: Introductionmentioning

confidence: 99%

Study of the Effect of Parietal Suction and Blowing on the Stability of Laminar External Flow

Laouer¹,

Mezaache²,

Laouar³

2016

IJHT

View full text Add to dashboard Cite

show abstract

“…The solution of the nonlinear Partial Differential Equations (PDEs) (13)-(15) has a boundary layer at which the solution varies rapidly and away from the layer the solution various slowly and hence accurate and efficient computational techniques are needed for solving the considered problem [47][48][49][50][51][52] . System (13)-(15) can be written as;…”

Section: Hybrid Linearization-chebyshev Spectral Methods (Hlcsm)mentioning

confidence: 99%

Magneto-Hybrid Nanofluids Flow via Mixed Convection past a Radiative Circular Cylinder

El‐Zahar

Rashad

Saad

et al. 2020

Sci Rep

View full text Add to dashboard Cite

The goal of the current analysis is to scrutinize the magneto-mixed convective flow of aqueous-based hybrid-nanofluid comprising Alumina and Copper nanoparticles across a horizontal circular cylinder with convective boundary condition. The energy equation is modelled by interpolating the non-linear radiation phenomenon with the assisting and opposing flows. The original equations describing the magneto-hybrid nanofluid motion and energy are converted into non-dimensional equations and solved numerically using a new hybrid linearization-Chebyshev spectral method (HLCSM). HLCSM is a high order spectral semi-analytical numerical method that results in an analytical solution in η-direction and thereby the solution is valid in overall the η-domain, not only at the grid points. The impacts of diverse parameters on the allied apportionment are inspected, and the fallouts are described graphically in the investigation. The physical quantities of interest containing the drag coefficient and the heat transfer rate are predestined versus fundamental parameters, and their outcomes are elucidated. It is witnessed that both drag coefficient and Nusselt number have greater magnitude for Cu-water followed by hybrid nanofluid and Al2O3-water. Moreover, the value of the drag coefficient declines versus the enlarged solid volume fraction. To emphasize the originality of the current analysis, the outcomes are compared with quoted works, and excellent accord is achieved in this consideration.

show abstract

“…The Chebyshev spectral collocation method [8,9] has been traditionally used to solved biharmonic problems. Its main advantage lies in the fact that it only needs a degree of freedom per node and it exhibits exponential convergence rates.…”

Section: Introductionmentioning

confidence: 99%

PGD for Solving the Biharmonic Equation

Chinesta

Leygue

et al. 2012

Volume 1: Advanced Computational Mechanics; Advanced Simulation-Based Engineering Sciences; Virtual and Augmented Reality; Appl

View full text Add to dashboard Cite

Biharmonic problem has been raised in many research fields, such as elasticity problem in plate geometries or the Stokes flow problem formulated by using the stream function. The fourth order partial differential equation can be solved by applying many techniques. When using finite elements C 1 continuity must be assured. For this purpose Hermite interpolations constitute an appealing choice, but it imply the consideration of many degrees of freedom at each node with the consequent impact on the resulting discrete linear problem. Spectral approaches allow exponential convergence whilst a single degree of freedom is needed. However, the enforcement of boundary conditions remains a tricky task. In this paper we propose a separated representation of the stream function which transform the 2D solution in a sequence of 1D problems, each one be solved by using a spectral approximation. INTRODUCTIONThe The spectral method has been widely used in the solution of Partial Differential Equations -PDE -, in particular high order PDEs, e.g. [7].The Chebyshev spectral collocation method [8,9] has been traditionally used to solved biharmonic problems. Its main advantage lies in the fact that it only needs a degree of freedom per node and it exhibits exponential convergence rates.In this paper spectral collocation schemes are combined with the PGD technique [10,11] that allows a separated representation of the fields involved in the model, and then in our case, transform the solution of a 2D model into the solution of few 1D problems.

show abstract

A chebyshev collocation spectral method for numerical simulation of incompressible flow problems

Cited by 16 publications

References 20 publications

Study of the Effect of Parietal Suction and Blowing on the Stability of Laminar External Flow

Study of the Effect of Parietal Suction and Blowing on the Stability of Laminar External Flow

Magneto-Hybrid Nanofluids Flow via Mixed Convection past a Radiative Circular Cylinder

PGD for Solving the Biharmonic Equation

Contact Info

Product

Resources

About