Spectral (finite) volume method for conservation laws on unstructured grids VI: Extension to viscous flow

Sun, Yuzhi; Wang, Zhi Jian; Liu, Yen

doi:10.1016/j.jcp.2005.10.019

Cited by 138 publications

(83 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The state-of-the-art applications of high-order and high-accurate methods in complex grids are still limited, while there are many kinds of high-order schemes, such as compact schemes [5][6][7]33,35], WCNSs [9,10], ENO [37,38] and WENO schemes [2,3,39,52,53], DG schemes [40-44, 48, 49, 51, 54], spectral methods (including spectral element (SE) [55], SV [56,57,110], spectral difference (SD) [58], staggered spectral methods [60]), gas-kinetic schemes (GKS) [61,[63][64][65], dispersion-relation-preserving (DRP) schemes [67], low dissipative high-order schemes [68], monotonicity preserving (MP) schemes [69,70], group velocity control (GVC) schemes [71,72], SPH methods [45,62], ALE methods [64][65][66]81], methods for multiphase flows [42,46,47], and many hybrid ones [73][74][75][76]. In most published articles and reviews, the flows are complex with shock...…”

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

confidence: 99%

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

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

confidence: 99%

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

show abstract

“…Recently, hybrid high-order methods [2,4,5] have been presented in the context of HDG methods. On the other hand, in order to develop high-order conservative schemes, Wang and his collaborators proposed and studied so-called spectral volume (SV) methods [22,25] and spectral difference (SD) methods [21]. These methods have been successfully applied to, but limited to, mostly hyperbolic conservation laws.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Spectral Difference Methods for an Elliptic Equation

Jeon

Park

Shin

2017

Computational Methods in Applied Mathematics

View full text Add to dashboard Cite

A locally conservative, hybrid spectral difference method (HSD) is presented and analyzed for the Poisson equation. The HSD is composed of two types of finite difference approximations; the cell finite difference and the interface finite difference. Embedded static condensation on cell interior unknowns considerably reduces the global couplings, resulting in the system of equations in the cell interface unknowns only. A complete ellipticity analysis is provided. The optimal order of convergence in the semi-discrete energy norms is proved. Several numerical results are given to show the performance of the method, which confirm our theoretical findings.

show abstract

“…Recently, new high-order unstructured grid methods, such as the discontinuous Galerkin (DG) method, 1,2) the spectral volume (SV) method, [3][4][5][6] the staggered grid multi-domain spectral or the spectral difference (SD) method, 7,8) and the flux reconstruction method 9) have been developed. These methods are expected to achieve the formal order of accuracy even on unstructured grids by introducing degrees of freedom (DOF) within each element for high-order reconstruction of the local solution.…”

Section: Introductionmentioning

confidence: 99%

“…In the case of k-exact FVM, communicating all data involving a high-order wide stencil across the inter-domain boundary will be complicated and can worsen parallel efficiency. In prior works, 4,6,11) the SV method was developed for the Euler and Navier-Stokes (NS) equations in 2D, and linear stability analysis was investigated by Van den Aveele et al 12) In our previous study, 13) a 3rd-order SV scheme for the compressible Euler equations was developed and used to obtain accurate flowfield around complex commercial aircraft configurations while deploying high-lift devices. Later, an implicit SV method was developed using a nonlinear LU-SGS scheme for solving the 3D NS equations.…”

Section: Introductionmentioning

confidence: 99%

RANS Simulation using the Spectral Volume Scheme on Unstructured Tetrahedral Grids

Haga

Furudate

Sawada

2014

AEROSPACE TECHNOLOGY JAPAN

View full text Add to dashboard Cite

A high-order aerodynamics simulation code for the Reynolds-averaged Navier-Stokes (RANS) equations is developed using the spectral volume (SV) method for unstructured tetrahedral meshes. A nonlinear LU-SGS implicit scheme is used to enhance convergence to the steady state solution, and a novel reconstruction limiter for the SV method is developed to improve the accuracy and the convergence property for flows with shock waves. The turbulent viscosity is modeled by the Spalart-Allmaras (SA) one-equation model. The developed code is validated for turbulent flow over a flat plate and assessed for a transonic flowfield over a wing studied in the third AIAA drag prediction workshop (DPW-3). Computations of a turbulent flow over high-lift devices are performed, and the ability to predict complicated flowfields is demonstrated favorably via comparison with the reference data. The developed code is fully parallelized for application to large-scale industrial problems by using domain decomposition and MPI.

show abstract

Spectral (finite) volume method for conservation laws on unstructured grids VI: Extension to viscous flow

Cited by 138 publications

References 33 publications

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

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

Hybrid Spectral Difference Methods for an Elliptic Equation

RANS Simulation using the Spectral Volume Scheme on Unstructured Tetrahedral Grids

Contact Info

Product

Resources

About