A p-multigrid spectral difference method with explicit and implicit smoothers on unstructured triangular grids

Liang, Chunlei; Kannan, Ravishekar; Wang, Zhi Jian

doi:10.1016/j.compfluid.2008.02.004

Cited by 75 publications

(46 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…However much further work is needed before their efficiency is on a par with that of the best geometric multigrid approaches. Studies to date indicate that using a judicious choice of explicit and implicit smoothers at various multigrid levels may help to circumvent memory related issues whilst maintaining a suitable rate of convergence [85] [80]. Also, studies indicate that a combination of both p-multigrid and geometric multigrid may be beneficial [91].…”

Section: Discussionmentioning

confidence: 99%

“…Although the implicit non-linear LU-SGS approach offered the fastest convergence, memory requirements for the p-multigrid scheme (with an explicit smoother) were far lower, implying that the latter may better suited for large scale 3D calculations. Finally in 2009, Liang, Kannan and Wang [80] presented a p-multigrid algorithm in a SD context to solve the Euler equations. The scheme utilized a mix of implicit and explicit smoothers at different multigrid levels (similar to the approach of Luo, Baum and Lohner [85]).…”

Section: Geometric Multigrid and P-multigrid Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Facilitating the Adoption of Unstructured High-Order Methods Amongst a Wider Community of Fluid Dynamicists

Vincent

Jameson

2011

Math. Model. Nat. Phenom.

View full text Add to dashboard Cite

Abstract. Theoretical studies and numerical experiments suggest that unstructured high-order methods can provide solutions to otherwise intractable fluid flow problems within complex geometries. However, it remains the case that existing high-order schemes are generally less robust and more complex to implement than their low-order counterparts. These issues, in conjunction with difficulties generating high-order meshes, have limited the adoption of high-order techniques in both academia (where the use of low-order schemes remains widespread) and industry (where the use of low-order schemes is ubiquitous). In this short review, issues that have hitherto prevented the use of high-order methods amongst a non-specialist community are identified, and current efforts to overcome these issues are discussed. Attention is focused on four areas, namely the generation of unstructured high-order meshes, the development of simple and efficient time integration schemes, the development of robust and accurate shock capturing algorithms, and finally the development of high-order methods that are intuitive and simple to implement. With regards to this final area, particular attention is focused on the recently proposed flux reconstruction approach, which allows various well known high-order schemes (such as nodal discontinuous Galerkin methods and spectral difference methods) to be cast within a single unifying framework. It should be noted that due to the experience of the authors the review is directed somewhat towards aerodynamic applications and compressible flow. However, many of the discussions have a wider applicability. Moreover, the tone of the review is intended to be generally accessible, such that an extended scientific community can gain insight into factors currently pacing the adoption of unstructured high-order methods.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Geometric Multigrid and P-multigrid Methodsmentioning

confidence: 99%

Facilitating the Adoption of Unstructured High-Order Methods Amongst a Wider Community of Fluid Dynamicists

Vincent

Jameson

2011

Math. Model. Nat. Phenom.

View full text Add to dashboard Cite

show abstract

“…It is worth to note that Kannan et al [107,108,113] have successfully blended p-multigrid approach with pre-conditions or implicit LU-SGS, and the convergence rate is drastically improved for bad and skewed unstructured grids. For more details about p-multigrid methods, please refer to [108,[111][112][113][114] and the references therein.…”

Section: High-order and High Accurate Cfd Methods For Complex Grid Prmentioning

confidence: 99%

“…Implicit LU-SGS is also successfully used for SD and SV, such as the methods in [107,108]. P-multigrid approach, where p is the order of polynomial degree, is widely employed in DG [111,112], SV [108], SD [113], SE [114], and some similar schemes to accelerate convergence rate. It is worth to note that Kannan et al [107,108,113] have successfully blended p-multigrid approach with pre-conditions or implicit LU-SGS, and the convergence rate is drastically improved for bad and skewed unstructured grids.…”

Section: High-order and High Accurate Cfd Methods For Complex Grid Prmentioning

confidence: 99%

“…P-multigrid approach, where p is the order of polynomial degree, is widely employed in DG [111,112], SV [108], SD [113], SE [114], and some similar schemes to accelerate convergence rate. It is worth to note that Kannan et al [107,108,113] have successfully blended p-multigrid approach with pre-conditions or implicit LU-SGS, and the convergence rate is drastically improved for bad and skewed unstructured grids. For more details about p-multigrid methods, please refer to [108,[111][112][113][114] and the references therein.…”

Section: High-order and High Accurate Cfd Methods For Complex Grid Prmentioning

confidence: 99%

See 1 more Smart Citation

High-Order and High Accurate CFD Methods and Their Applications for Complex Grid Problems

Deng

Mao

et al. 2012

Commun. comput. phys.

View full text Add to dashboard Cite

Abstract. The purpose of this article is to summarize our recent progress in high-order and high accurate CFD methods for flow problems with complex grids as well as to discuss the engineering prospects in using these methods. Despite the rapid development of high-order algorithms in CFD, the applications of high-order and high accurate methods on complex configurations are still limited. One of the main reasons which hinder the widely applications of these methods is the complexity of grids. Many aspects which can be neglected for low-order schemes must be treated carefully for high-order ones when the configurations are complex. In order to implement highorder finite difference schemes on complex multi-block grids, the geometric conservation law and block-interface conditions are discussed. A conservative metric method is applied to calculate the grid derivatives, and a characteristic-based interface condition is employed to fulfil high-order multi-block computing. The fifth-order WCNS-E-5 proposed by Deng [9, 10] is applied to simulate flows with complex grids, including a double-delta wing, a transonic airplane configuration, and a hypersonic X-38 configuration. The results in this paper and the references show pleasant prospects in engineering-oriented applications of high-order schemes.

show abstract

An implicit LU‐SGS spectral volume method for the moment models in device simulations: Formulation in 1D and application to a p‐multigrid algorithm

Kannan

2011

Numer Methods Biomed Eng

View full text Add to dashboard Cite

SUMMARYA high-order spectral volume (SV) method was implemented for solving the steady-state moment models, such as the hydrodynamic (HD) models and the energy transport (ET) models for semiconductor device simulations (in 1D). The first derivative inviscid/convective fluxes are handled using an approximate Riemann flux and the second derivative diffusive fluxes are discretized using the local discontinuous Galerkin formulation (LDG). The LDG method is also used for discretizing the potential equation. An implicit pre-conditioned LU-SGS p-multigrid method developed for the SV Navier-Stokes (NS) solver by Kannan and Wang is adopted here for time marching. The entire formulation is compact and hence can be easily parallelized. A n + -n-n + diode was assumed for simulation purposes and the results are compared with the existing discontinuous Galerkin simulation results. In general, the numerical results are very promising and indicate that the approach has a great potential for higher-dimensional device problems.

show abstract

A p-multigrid spectral difference method with explicit and implicit smoothers on unstructured triangular grids

Cited by 75 publications

References 27 publications

Facilitating the Adoption of Unstructured High-Order Methods Amongst a Wider Community of Fluid Dynamicists

Facilitating the Adoption of Unstructured High-Order Methods Amongst a Wider Community of Fluid Dynamicists

High-Order and High Accurate CFD Methods and Their Applications for Complex Grid Problems

An implicit LU‐SGS spectral volume method for the moment models in device simulations: Formulation in 1D and application to a p‐multigrid algorithm

Contact Info

Product

Resources

About