Enhanced solution of 2D incompressible Navier–Stokes equations based on an immersed-boundary generalized harmonic polynomial cell method

Yu, Xueying; Fuhrman, David R.; Shao, Yanlin; Liao, Kangping; Duan, Wenyang; Zhang, Yunxing

doi:10.1016/j.euromechflu.2021.04.009

Cited by 7 publications

(7 citation statements)

References 57 publications

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“…Recently, the GHPC method has been successfully applied in solving the 2D Navier-Stokes equations based on the three-step projection method on uniform grids. Encouraging results have been achieved for all studied cases, including the Taylor-Green vortex, lid-driven cavity flow, and flow around a smooth circular cylinder [20]. They also made direct comparison with Navier-Stokes equations solver applying second-order FDM for the Poisson equation, and demonstrated that the accuracy of the pressure solution can be greatly improved by applying the more accurate GHPC method for the Poisson equation.…”

Section: Introductionmentioning

confidence: 83%

“…The Poisson equation Eq. ( 7) will be solved by the immersed-boundary GHPC method [20], while all advection terms in Eq. ( 3) are discretized by the secondorder explicit QUICK scheme, and the diffusion terms on the right hand side of Eq.…”

Section: The Numerical Model 21 Governing Equationsmentioning

confidence: 99%

“…In this paper, we will also use the immersed-boundary strategy for both pressure and velocity fields. More details of the immersed-boundary GHPC method can be found in [20]. Only uniform cells were considered in most of the analyses in [19] where the GHPC method was developed.…”

Section: Introductionmentioning

confidence: 99%

“…Only uniform cells were considered in most of the analyses in [19] where the GHPC method was developed. The recent application of the GHPC method in solving Navier-Stokes equation by Yu et al [20] also only operated on the uniform grids. To date, the accuracy properties of the GHPC method are still not fully understood, in particular on non-uniform grids, where we have seen loss of accuracy in the original HPC method.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, as an important extension of the work of [19] and [20], the properties of both local and global accuracy for the GHPC method on non-uniform grids will be assessed in detail. Cases with analytical solutions will be considered, and comparison with the second-order FDM method, which is widely used for spatial discretization in Navier-Stokes equations solvers will be made.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Solutions of Two-Dimensional Navier–Stokes Equations Based on a Generalized Harmonic Polynomial Cell Method With Non-Uniform Grid

Shao

Fuhrman

2022

Journal of Offshore Mechanics and Arctic Engineering

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It is essential for a Navier-Stokes equations solver based on a projection method to be able to solve the resulting Poisson equation accurately and efficiently. In this paper, we present numerical solutions of the 2D Navier-Stokes equations using the fourth-order generalized harmonic polynomial cell (GHPC) method as the Poisson equation solver. Particular focus is on the local and global accuracy of the GHPC method on non-uniform grids. Our study reveals that the GHPC method enables use of more stretched grids than the original HPC method. Compared with a second-order central finite difference method (FDM), global accuracy analysis also demonstrates the advantage of applying the GHPC method on stretched non-uniform grids. An immersed boundary method is used to deal with general geometries involving the fluid-structure-interaction problems. The Taylor-Green vortex and flow around a smooth circular cylinder and square are studied for the purpose of verification and validation. Good agreement with reference results in the literature confirms the accuracy and efficiency of the new 2D Navier-Stokes equation solver based on the present immersed-boundary GHPC method utilizing non-uniform grids. The present Navier-Stokes equations solver uses second-order FDM for the discretization of the diffusion and advection terms, which may be replaced by other higher-order schemes to further improve the accuracy.

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Section: Introductionmentioning

confidence: 83%

Section: The Numerical Model 21 Governing Equationsmentioning

confidence: 99%