Multigrid Euler calculations over complete aircraft

Tidd, D. M.; Strash, Daniel J.; Epstein, Boris; Luntz, A.; Nachshon, A.; Rubin, T.

doi:10.2514/3.46288

Cited by 12 publications

(7 citation statements)

References 2 publications

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“…Instead of a finite-volume approach, Tidd et al [4] used a finite difference formulation to treat the boundary conditions. They introduced the concept of a ''multi-valued dummy point''.…”

Section: Introductionmentioning

confidence: 99%

“…Solution methods using a Cartesian mesh in computational fluid dynamics simulations are popular with many investigators [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], and have numerous inherent advantages. These include simple and efficient field mesh generation, superior implementation of high order discretization schemes, minimal phase error associated with shock-capturing calculations, and an absence of issues associated with mesh skewness and distortion.…”

Section: Introductionmentioning

confidence: 99%

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A gridless boundary condition method for the solution of the Euler equations on embedded Cartesian meshes with multigrid

Kirshman

Liu

2004

Journal of Computational Physics

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“…Instead of a finite-volume approach, Tidd et al [4] used a finite difference formulation to treat the boundary conditions. They introduced the concept of a ''multi-valued dummy point''.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A gridless boundary condition method for the solution of the Euler equations on embedded Cartesian meshes with multigrid

Kirshman

Liu

2004

Journal of Computational Physics

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“…Multigrid acceleration can be implemented in the framework of embedded grids. 12 Furthermore, Cartesian grids offer considerable ease in implementing higher-order schemes. However, the main challenge in using a Cartesian method is in dealing with arbitrary boundaries.…”

Section: Introductionmentioning

confidence: 99%

“…11,12,20 Halo points might need to be used in such an approach. Unlike the cut-cells method, this method is not conservative and requires special treatment for regions with thin surfaces (e.g., a trailing edge) where multiple values are defined at a particular point.…”

Section: Introductionmentioning

confidence: 99%

“…Unlike the cut-cells method, this method is not conservative and requires special treatment for regions with thin surfaces (e.g., a trailing edge) where multiple values are defined at a particular point. 11,12 To minimize the lack of conservation, higher-order representation for the boundary is used to improve solution accuracy as seen in the work of Forrer and Jeltsch. 21 An alternative to reducing the effort associated with mesh generation is the use of a purely gridless approach for the entire computational domain (e.g., Refs.…”

Section: Introductionmentioning

confidence: 99%

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Euler Solution Using Cartesian Grid with a Gridless Least-Squares Boundary Treatment

2005

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An approach that uses gridless or meshless methods to address the problem of boundary implementation associated with the use of Cartesian grid is discussed. This method applies the gridless concept only at the interface, whereas a standard structured grid method is used everywhere else. The Cartesian grid is used to specify and distribute the computational points on the boundary surface but not to define the geometrical properties. Euler fluxes for the neighbors of cut cells are computed using the gridless method involving a local least-squares curve fit of a "cloud" of grid points. The boundary conditions implemented on the surface points are automatically satisfied in the process of evaluating the surface values in a similar least-squares fashion. The present method does not require the use of halo points. Subsonic, transonic, and supersonic flows are computed for the NACA 0012 and RAE 2822 airfoils, and the results compare well with solutions obtained by a standard Euler solver on body-fitted grids. The method is also used to calculate the flow over a three-element airfoil configuration, and the result is compared with the exact solution for this configuration obtained by conformal mapping.

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A cell-based smoothed finite element method for three-dimensional incompressible flows using Cartesian cut-cell meshes

Wang,

Song,

Zhou

et al. 2024

Physics of Fluids

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Cartesian cut-cell meshes are favored for their excellent complex geometric adaptability, orthogonality, and mesh generation convenience. However, the difficulty in constructing shape function for hanging-node and irregular cut-cell elements limits their use in a standard finite element method (FEM). Inspired by the point interpolation method shape function used in a smoothed finite element method (S-FEM) which adapts to the arbitrary shape of an element, this work proposes a cell-based S-FEM using Cartesian cut-cell meshes for incompressible flows. Four different types of cell-based smoothing domains (CSDs) are constructed and compared in the Cartesian cut-cell mesh, involving node-based CSD (NCSD), face-based CSD (FCSD), mixed CSD (MIXCSD), and tetrahedral CSD (T4CSD). The smoothed Galerkin weak form and semi-implicit characteristic-based split (CBS) scheme are employed for spatial discretization and stabilization of Naiver–Stokes (N–S) equations, respectively. Several numerical examples are utilized to compare the convergences, computational accuracy, and computational efficiency of proposed CSDs. The numerical results demonstrate that FCSD and T4CSD exhibit instability. Conversely, NCSD and MIXCSD exhibit good stability, and NCSD shows slightly higher computational accuracy than MIXCSD, but at a lower computational efficiency. Additionally, the results show that Cartesian cut-cell meshes offer superior computational accuracy compared to tetrahedral meshes. Therefore, the present method provides an attractive numerical technique for solving flow problems with complex geometries.

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Multigrid Euler calculations over complete aircraft

Cited by 12 publications

References 2 publications

A gridless boundary condition method for the solution of the Euler equations on embedded Cartesian meshes with multigrid

A gridless boundary condition method for the solution of the Euler equations on embedded Cartesian meshes with multigrid

Euler Solution Using Cartesian Grid with a Gridless Least-Squares Boundary Treatment

A cell-based smoothed finite element method for three-dimensional incompressible flows using Cartesian cut-cell meshes

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