A new Green–Gauss reconstruction on unstructured meshes. Part I: Gradient reconstruction

Deka, Mandeep; Brahmachary, Shuvayan; Thirumalaisamy, Ramakrishnan; Dalal, Amaresh; Natarajan, Ganesh

doi:10.1016/j.jcp.2018.10.023

Cited by 18 publications

(21 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Least Square (LSQR) gradient reconstruction [38][39][40] is commonly used in the second-order unstructured finite volume methods [13,14,18,41]. 2 2 2 2 2 3 3 3 3 3 .…”

Section: K-exact Reconstruction Based On Any Local Originsmentioning

confidence: 99%

Extending the global-direction stencil with "face-area-weighted centroid" to unstructured finite volume discretization from integral form

Kong

Dong²,

Liu

et al. 2020

Preprint

View full text Add to dashboard Cite

Accuracy of unstructured finite volume discretization is greatly influenced by the gradient reconstruction. For the commonly used k-exact reconstruction method, the cell centroid is always chosen as the reference point to formulate the reconstructed function. But in some practical problems, such as the boundary layer, cells in this area are always set with high aspect ratio to improve the local field resolution, and if geometric centroid is still utilized for the spatial discretization, the severe grid skewness cannot be avoided, which is adverse to the numerical performance of unstructured finite volume solver. In previous work [Chinese Physics B. 2020, In press], we explored a novel global-direction stencil and combined it with the face-area-weighted centroid on unstructured finite volume methods from differential form to realize the skewness reduction and a better reflection of flow anisotropy. Greatly inspired by the differential form, in this research, we demonstrate that it is also feasible to extend this novel method to the unstructured finite volume discretization from integral form on both second and third-order finite volume solver. Numerical examples governed by linear convective, Euler and Laplacian equations are utilized to examine the correctness as well as effectiveness of this extension. Compared with traditional vertex-neighbor and face-neighbor stencils based on the geometric centroid, the grid skewness is almost eliminated and computational accuracy as well as convergence rate is greatly improved by the global-direction stencil with face-area-weighted centroid. As a result, on unstructured finite volume discretization from integral form, the method also has superiorities on both computational accuracy and convergence rate.

show abstract

“…Least Square (LSQR) gradient reconstruction [38][39][40] is commonly used in the second-order unstructured finite volume methods [13,14,18,41]. 2 2 2 2 2 3 3 3 3 3 .…”

Section: K-exact Reconstruction Based On Any Local Originsmentioning

confidence: 99%

Extending the global-direction stencil with "face-area-weighted centroid" to unstructured finite volume discretization from integral form

Kong

Dong²,

Liu

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Least Square (LSQR) gradient reconstruction [38][39][40] is commonly used in the second-order unstructured finite volume methods [13,14,18,41]. Note, however, that for integral finite volume discretization, the real point value utilized in reconstruction and flux evaluation process is always…”

Section: K-exact Reconstruction Based On Any Local Originsmentioning

confidence: 99%

Extending the global-direction stencil with "face-area-weighted centroid" to unstructured finite volume discretization from integral form

Kong

Dong

Liu

et al. 2020

Preprint

View full text Add to dashboard Cite

Accuracy of unstructured finite volume discretization is greatly influenced by the gradient reconstruction. For the commonly used k-exact reconstruction method, the cell centroid is always chosen as the reference point to formulate the reconstructed function. But in some practical problems, such as the boundary layer, cells in this area are always set with high aspect ratio to improve the local field resolution, and if geometric centroid is still utilized for the spatial discretization, the severe grid skewness cannot be avoided, which is adverse to the numerical performance of unstructured finite volume solver. In previous work, we explored a novel global-direction stencil and combine it with face-area-weighted centroid on unstructured finite volume methods from differential form to realize the skewness reduction and a better reflection of flow anisotropy. Note, however, that the differential form is hard to achieve higher-order accuracy, and in order to set stage for the method promotion on higher-order numerical simulation, in this research, we demonstrate that it is also feasible to extend this novel method to the unstructured finite volume discretization in integral form. Numerical examples governed by linear convective, Euler and Laplacian equations are utilized to examine the correctness as well as effectiveness of this extension. Compared with traditional vertex-neighbor and face-neighbor stencils based on the geometric centroid, the grid skewness is almost eliminated and computational accuracy as well as convergence rate is greatly improved by the global-direction stencil with face-area-weighted centroid. As a result, on unstructured finite volume discretization from integral form, the method also has a better numerical performance.

show abstract

“…Least Square (LSQR) gradient reconstruction [38][39][40] is commonly used in the secondorder unstructured finite volume methods [13,14,18,41].…”

Section: K-exact Reconstruction Based On Any Local Originsmentioning

confidence: 99%

Extending the global-direction stencil with “face-area-weighted centroid” to unstructured finite volume discretization from integral form

et al. 2020

View full text Add to dashboard Cite

Accuracy of unstructured finite volume discretization is greatly influenced by the gradient reconstruction. For the commonly used k-exact reconstruction method, the cell centroid is always chosen as the reference point to formulate the reconstructed function. But in some practical problems, such as the boundary layer, cells in this area are always set with high aspect ratio to improve the local field resolution, and if geometric centroid is still utilized for the spatial discretization, the severe grid skewness cannot be avoided, which is adverse to the numerical performance of unstructured finite volume solver. In previous work [Kong, et al. Chin Phys B 29(10):100203, 2020], we explored a novel global-direction stencil and combined it with the face-area-weighted centroid on unstructured finite volume methods from differential form to realize the skewness reduction and a better reflection of flow anisotropy. Greatly inspired by the differential form, in this research, we demonstrate that it is also feasible to extend this novel method to the unstructured finite volume discretization from integral form on both second and third-order finite volume solver. Numerical examples governed by linear convective, Euler and Laplacian equations are utilized to examine the correctness as well as effectiveness of this extension. Compared with traditional vertex-neighbor and face-neighbor stencils based on the geometric centroid, the grid skewness is almost eliminated and computational accuracy as well as convergence rate is greatly improved by the global-direction stencil with face-area-weighted centroid. As a result, on unstructured finite volume discretization from integral form, the method also has superiorities on both computational accuracy and convergence rate.

show abstract

A new Green–Gauss reconstruction on unstructured meshes. Part I: Gradient reconstruction

Cited by 18 publications

References 21 publications

Extending the global-direction stencil with "face-area-weighted centroid" to unstructured finite volume discretization from integral form

Extending the global-direction stencil with "face-area-weighted centroid" to unstructured finite volume discretization from integral form

Extending the global-direction stencil with "face-area-weighted centroid" to unstructured finite volume discretization from integral form

Extending the global-direction stencil with “face-area-weighted centroid” to unstructured finite volume discretization from integral form

Contact Info

Product

Resources

About