First-order accurate finite difference schemes for boundary vorticity approximations in curvilinear geometries

Siyyam, Hani I.; Ford, R. A.; Hamdan, M. H.

doi:10.1016/j.amc.2009.08.028

Cited by 3 publications

(8 citation statements)

References 13 publications

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“…Based on the above description, Siyyam, Ford and Hamdan, [12], observed the following: 1) The relationship between the order of the scheme, n, and the minimum number, k, of grid points used is that 1 k n = + . This will render system (28) determinate consisting of n + 1 equations in as many unknowns.…”

Section: Derivation Of Finite Difference Schemesmentioning

confidence: 99%

“…In order to derive forward differencing schemes of local accuracy n for the first derivative along the grid line (i,1) using max k grid points, Siyyam, Ford and Hamdan, [12], assumed the schemes to take the form:…”

Section: Derivation Of Finite Difference Schemesmentioning

confidence: 99%

“…In order to overcome the above shortcomings, forward and backward finite difference schemes of various orders of local accuracy continue to be developed to better capture the boundary effects (including better approximation to the vorticiy on a solid boundary), [12]. A large number of research articles has dealt with the testing of high order (although mainly second-and third-order) schemes when a non-uniform grid is employed (cf.…”

Section: Introductionmentioning

confidence: 99%

“…Numerical solution is then sought for transformed governing equations and boundary conditions, [1] [5]- [7] [9] [12] [15] [16]. In particular, the vorticity Neumann boundary condition is transformed into the new coordinate system and a suitable differencing scheme is employed to accurately approximate the boundary vorticity.…”

Section: Introductionmentioning

confidence: 99%

“…This is due to the fact that when a uniform grid is chosen in the physical domain, use of the von Mises transformation produces a naturally smooth clustered grid in the computational domain. In the above previous work, [12] [16], schemes of first-, second-and third-order local accuracy were developed for the first derivative and used in the calculation of vorticity on the flow domain boundary. In those schemes, stencils involving up to five computational grid points were used, and a comparison was offered between uniform and non-uniform grids.…”

Section: Introductionmentioning

confidence: 99%

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High-Order Finite Difference Schemes for the First Derivative in Von Mises Coordinates

Alharbi¹,

Hamdan²

2016

JAMP

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Third-and fourth-order accurate finite difference schemes for the first derivative of the square of the speed are developed, for both uniform and non-uniform grids, and applied in the study of a two-dimensional viscous fluid flow through an irregular domain. The von Mises transformation is used to transform the governing equations, and map the irregular domain onto a rectangular computational domain. Vorticity on the solid boundary is expressed in terms of the first partial derivative of the square of the speed of the flow in the computational domain, and the schemes are used to calculate the vorticity at the computational boundary grid points using up to five computational domain grid points. In all schemes developed, we study the effect of coordinate clustering on the computed results.

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Section: Derivation Of Finite Difference Schemesmentioning

confidence: 99%

Section: Derivation Of Finite Difference Schemesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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High-Order Finite Difference Schemes for the First Derivative in Von Mises Coordinates

Alharbi¹,

Hamdan²

2016

JAMP

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Effects of Physical Coordinate Clustering on Boundary Vorticity Approximations in von Mises Coordinates

Hamdan

2021

Wseas Transactions on Fluid Mechanics

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Forward finite difference expressions of first-order accuracy for boundary vorticity on a solid boundary are evaluated in this work when the physical coordinates are clustered and mapped using von Mises coordinates. Results show that schemes using in-field grid points do not improve solutions obtained. Results also show that the finer the grid used in the physical domain, and the more clustered it is, improves the boundary vorticity values in the computational domain. The “best” expressions forward finite difference expressions are identified when two, three, four and five grid points are used.

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A Fifth-Order-Accurate Finite Difference Scheme for a Natural Coordinate System with Non-Uniform Grid

Gadoura

Hamdan

2022

Equations

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First-order accurate finite difference schemes for boundary vorticity approximations in curvilinear geometries

Cited by 3 publications

References 13 publications

High-Order Finite Difference Schemes for the First Derivative in Von Mises Coordinates

High-Order Finite Difference Schemes for the First Derivative in Von Mises Coordinates

Effects of Physical Coordinate Clustering on Boundary Vorticity Approximations in von Mises Coordinates

A Fifth-Order-Accurate Finite Difference Scheme for a Natural Coordinate System with Non-Uniform Grid

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