A compact scheme for the streamfunction-velocity formulation of the 2D steady incompressible Navier-Stokes equations in polar coordinaes

Yu, Peixiang; Tian, Zhenfu

doi:10.1007/s10915-012-9667-7

Cited by 16 publications

(14 citation statements)

References 32 publications

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“…With the increase of Reynolds number, it is clear that the two eddies grow large. All the flow patterns are in accord with other scholars research . Quantitative comparisons of our method with other researches for the hydrodynamic coefficients and the locations of the separation and reattachment points for Re D =10, 20, and 40 are listed in Table .…”

Section: Numerical Experimentssupporting

confidence: 79%

“…We assume the cylinder to be of unit diameter ( D =1) placed in an infinite domain, and the outer radius we set R ∞ =20, which is 40 times the radius of the cylinder ( R c =0.5). According to Yu and Tian, the choice of R ∞ =20 is enough. For this problem, the Reynolds numbers is defined as

R e_{D} = \frac{U_{\infty} D}{ν}

.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…However, different from other compact schemes, in that work, the second‐order central difference rather than the fourth‐order compact scheme is adopted for the first‐order partial derivative and used to establish the discretization of the fourth‐order partial derivatives of the stream function, which would result in lower accuracy. In 2013, we developed a second‐order compact scheme for the stream function‐velocity formulation of the steady N‐S equation on polar coordinates . In that method, the first‐order partial derivatives of the stream function were approximated by the fourth‐order accurate Páde scheme.…”

Section: Introductionmentioning

confidence: 99%

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A high‐order compact scheme for solving the 2D steady incompressible Navier‐Stokes equations in general curvilinear coordinates

Chen

Tian

et al. 2019

Numerical Methods in Fluids

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Summary In this paper, a high‐order compact finite difference algorithm is established for the stream function‐velocity formulation of the two‐dimensional steady incompressible Navier‐Stokes equations in general curvilinear coordinates. Different from the previous work, not only the stream function and its first‐order partial derivatives but also the second‐order mixed partial derivative is treated as unknown variable in this work. Numerical examples, including a test problem with an analytical solution, three types of lid‐driven cavity flow problems with unusual shapes and steady flow past a circular cylinder as well as an elliptic cylinder with angle of attack, are solved numerically by the newly proposed scheme. For two types of the lid‐driven trapezoidal cavity flow, we provide the detailed data using the fine grid sizes, which can be considered the benchmark solutions. The results obtained prove that the present numerical method has the ability to solve the incompressible flow for complex geometry in engineering applications, especially by using a nonorthogonal coordinate transformation, with high accuracy.

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Section: Numerical Experimentssupporting

confidence: 79%

R e_{D} = \frac{U_{\infty} D}{ν}

.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A high‐order compact scheme for solving the 2D steady incompressible Navier‐Stokes equations in general curvilinear coordinates

Chen

Tian

et al. 2019

Numerical Methods in Fluids

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“…For the solution of the semicircular cavity flow problem, the streamfunction and vorticity equations are solved iteratively up to large Reynolds numbers. The present numerical results are compared in detail with the results of [10,12,14,15]. For the flows in enclosures, Batchelor's mean square law ( [29]) states that the flow, which is coupled to the solid wall velocities at the boundaries, should have a solid body motion inside the enclosure with a uniform vorticity at large Reynolds numbers and the flow quantities should converge to the limiting values.…”

Section: Introductionmentioning

confidence: 98%

“…Later, Yang et al [11,12] and Ding et al [13] numerically studied the same flow problem using the Lattice Boltzmann method. Also, Yu et al [14] solved the Navier-Stokes equations in polar coordinates using a compact difference scheme and simulated the semi-circular cavity flow problem.…”

Section: Introductionmentioning

confidence: 99%

Stationary solutions of incompressible viscous flow in a wall-driven semi-circular cavity

Ertürk

2021

Acta Polytech

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Stationary numerical solutions of incompressible viscous flow inside a wall-driven semicircular cavity are presented. After a conformal mapping of the geometry, using a body-fitted mesh, the Navier-Stokes equations are solved numerically. The stationary solutions of the flow in a wall-driven semi-circular cavity are computed up to Re = 24000. The present results are in good agreement with the published results found in the literature. Our results show that as the Reynolds number increases, the sizes of the secondary and tertiary vortices increase, whereas the size of the primary vortex decreases. At large Reynolds numbers, the vorticity at the primary vortex centre increases almost linearly stating that Batchelor’s mean-square law is not valid for wall-driven semi-circular cavity flow. Detailed results are presented and also tabulated for future references and benchmark purposes.

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A Symbolic-Numeric Method for Solving the Poisson Equation in Polar Coordinates

Vorozhtsov

2023

Computer Algebra in Scientific Computing

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A compact scheme for the streamfunction-velocity formulation of the 2D steady incompressible Navier-Stokes equations in polar coordinaes

Cited by 16 publications

References 32 publications

A high‐order compact scheme for solving the 2D steady incompressible Navier‐Stokes equations in general curvilinear coordinates

A high‐order compact scheme for solving the 2D steady incompressible Navier‐Stokes equations in general curvilinear coordinates

Stationary solutions of incompressible viscous flow in a wall-driven semi-circular cavity

A Symbolic-Numeric Method for Solving the Poisson Equation in Polar Coordinates

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