High-Order Multidomain Spectral Difference Method for the Navier-Stokes Equations

Sun, Yuzhi; Wang, Z. J.; Liu, Yen

doi:10.2514/6.2006-301

Cited by 111 publications

(173 citation statements)

References 26 publications

(39 reference statements)

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“…In contrast to DG schemes (for which the treatment of viscous terms is somewhat involved), SD type schemes are able to accommodate viscous terms in a simple fashion [123]. The FR approach potentially offers an equally simple way to treat viscous terms [59].…”

Section: Flux Reconstruction For Viscous Termsmentioning

confidence: 99%

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

Vincent

Jameson

2011

Math. Model. Nat. Phenom.

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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.

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Section: Flux Reconstruction For Viscous Termsmentioning

confidence: 99%

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

Vincent

Jameson

2011

Math. Model. Nat. Phenom.

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“…The formulation of the equations for the 2D spectral difference scheme on quadrilateral meshes is similar to the formulation of Sun et al 3 for unstructured hexahedral grids Consider the unsteady compressible 2D Navier Stokes equations in conservative form…”

Section: Formulation Of 2d Spectral Difference Scheme On Quadrilamentioning

confidence: 99%

“…2,3 Even though this approach is easy to implement, the computational effort involved is large since each variable at each solution point has to be changed, and the residuals recomputed. Numerical tests have shown that it is not necessary to compute the Jacobian matrix at every iteration.…”

Section: Implicit Schemementioning

confidence: 99%

“…It was originally proposed by Liu et al 4 and developed for wave equations in their paper on triangular grids. Wang et al 5 (2007) extended it to 2D Euler equations on triangular grids and Sun et al 3 (2007) further developed it for three-dimensional Navier-Stokes equations on hexahedral unstructured meshes. The SD method combines elements from finite-volume and finite-difference techniques, and is particularly attractive because it is conservative, and has a simple formulation and implementation.…”

Section: Introductionmentioning

confidence: 99%

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A p-Multigrid Spectral Difference Method For Viscous Compressible Flow Using 2D Quadrilateral Meshes

Premasuthan

Liang

et al. 2009

47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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The work focuses on the development of a 2D quadrilateral element based Spectral Difference solver for viscous flow calculations, and the application of the p-multigrid method and implicit time-stepping to accelerate convergence. This paper extends the previous work by Liang et al (2009) on the p-multigrid method for 2D inviscid compressible flow, 2 to viscous flows. The high-order spectral difference solver for unstructured quadrilateral meshes is based on the formulation of Sun et al 3 for unstructured hexahedral elements. The p-multigrid method operates on a sequence of solution approximations of different polynomial orders ranging from one upto four. An efficient preconditioned Lower-Upper Symmetric Gauss-Seidel (LU-SGS) implicit scheme is also implemented. The spectral difference method is applied to a variety of inviscid and viscous compressible flow problems. The speed-up using the p-Multigrid and Implicit time-stepping techniques is also demonstrated.

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“…The solver, which is based on the approach presented by Wang [19], can run on meshes containing both straight-sided and curved-sided quadrilateral elements. An methodology for applying the code to unstructured mixed meshes containing both triangular and quadrangular elements has also been developed [20].…”

Section: Code Development 231 Two-dimensional Compressible Viscous mentioning

confidence: 99%

High-Order Numerical Algorithms for Steady and Unsteady Simulation of Viscous Compressible Flow with Shocks

Jameson¹,

Vincent²

2010

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High-Order Multidomain Spectral Difference Method for the Navier-Stokes Equations

Cited by 111 publications

References 26 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

A p-Multigrid Spectral Difference Method For Viscous Compressible Flow Using 2D Quadrilateral Meshes

High-Order Numerical Algorithms for Steady and Unsteady Simulation of Viscous Compressible Flow with Shocks

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