Velocity-correction schemes for the incompressible Navier–Stokes equations in general coordinate systems

Serson, Douglas; Meneghini, Júlio Romano; Sherwin, Spencer J.

doi:10.1016/j.jcp.2016.04.026

Cited by 30 publications

(33 citation statements)

References 9 publications

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“…With S known, E n+1 can be computed based on equation (35), and R n+1 can be computed using equation (21). The velocity u n+1 and pressure p n+1 are then given by equations (33) and (28).…”

Section: Solution Algorithm and Implementationmentioning

confidence: 99%

Numerical approximation of incompressible Navier-Stokes equations based on an auxiliary energy variable

Lin

Yang

Dong

2019

Journal of Computational Physics

124

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We present a numerical scheme for approximating the incompressible Navier-Stokes equations based on an auxiliary variable associated with the total system energy. By introducing a dynamic equation for the auxiliary variable and reformulating the Navier-Stokes equations into an equivalent system, the scheme satisfies a discrete energy stability property in terms of a modified energy and it allows for an efficient solution algorithm and implementation. Within each time step, the algorithm involves the computations of two pressure fields and two velocity fields by solving several de-coupled individual linear algebraic systems with constant coefficient matrices, together with the solution of a nonlinear algebraic equation about a scalar number involving a negligible cost. A number of numerical experiments are presented to demonstrate the accuracy and the performance of the presented algorithm.

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“…With S known, E n+1 can be computed based on equation (35), and R n+1 can be computed using equation (21). The velocity u n+1 and pressure p n+1 are then given by equations (33) and (28).…”

Section: Solution Algorithm and Implementationmentioning

confidence: 99%

Numerical approximation of incompressible Navier-Stokes equations based on an auxiliary energy variable

Lin

Yang

Dong

2019

Journal of Computational Physics

124

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“…Accordingly, the velocity components and pressure are transformed as follows (Serson, Meneghini & Sherwin 2016):…”

Section: Mathematical Formulationmentioning

confidence: 99%

Destabilisation and modification of Tollmien–Schlichting disturbances by a three-dimensional surface indentation

Mughal

Gowree

et al. 2017

J. Fluid Mech.

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We consider the influence of a smooth three-dimensional (3-D) indentation on the instability of an incompressible boundary layer by linear and nonlinear analyses. The numerical work was complemented by an experimental study to investigate indentations of approximately 11δ 99 and 22δ 99 width at depths of 45 %, 52 % and 60 % of δ 99 , where δ 99 indicates 99% boundary layer thickness. For these indentations a separation bubble confined within the indentation arises. Upstream of the indentation, spanwise-uniform Tollmien-Schlichting (TS) waves are assumed to exist, with the objective to investigate how the 3-D surface indentation modifies the 2-D TS disturbance. Numerical corroboration against experimental data reveals good quantitative agreement. Comparing the structure of the 3-D separation bubble to that created by a purely 2-D indentation, there are a number of topological changes particularly in the case of the widest indentation; more rapid amplification and modification of the upstream TS waves along the symmetry plane of the indentation is observed. For the shortest indentations, beyond a certain depth there are then no distinct topological changes of the separation bubbles and hence on flow instability. The destabilising mechanism is found to be due to the confined separation bubble and is attributed to the inflectional instability of the separated shear layer. Finally for the widest width indentation investigated (22δ 99 ), results of the linear analysis are compared with direct numerical simulations. A comparison with the traditional criteria of using N-factors to assess instability of properly 3-D disturbances reveals that a general indication of flow destabilisation and development of strongly nonlinear behaviour is indicated as N = 6 values are attained. However N-factors, based on linear models, can only be used to provide indications and severity of the destabilisation, since the process of disturbance breakdown to turbulence is inherently nonlinear and dependent on the magnitude and scope of the initial forcing.

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“…The incompressible Navier-Stokes and continuity equations in (2.6) and (2.7) are solved using the high-order spectral/hp element library Nektar++ (Cantwell et al 2015). Using the formulation in Serson, Meneghini & Sherwin (2016), the equations are first transformed to generalized coordinates (x,ȳ,z) via…”

Section: Numerical Detailsmentioning

confidence: 99%

Receptivity and transition in a solitary wave boundary layer over random bottom topography

Önder

Liu

2021

J. Fluid Mech.

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Velocity-correction schemes for the incompressible Navier–Stokes equations in general coordinate systems

Cited by 30 publications

References 9 publications

Numerical approximation of incompressible Navier-Stokes equations based on an auxiliary energy variable

Numerical approximation of incompressible Navier-Stokes equations based on an auxiliary energy variable

Destabilisation and modification of Tollmien–Schlichting disturbances by a three-dimensional surface indentation

Receptivity and transition in a solitary wave boundary layer over random bottom topography

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