Geometric conservation law and applications to high-order finite difference schemes with stationary grids

Deng, Xiaogang; Mao, Meiliang; Tu, Guohua; Liu, Huayong; Zhang, Hanxin

doi:10.1016/j.jcp.2010.10.028

Cited by 140 publications

(80 citation statements)

References 38 publications

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“…Our experiences show that low quality grids bear large GCLrelated errors than that of high-quality grids. A general condition to satisfy the GCL in FDM has been derived by Deng et al [100].…”

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

confidence: 99%

“…This difficult is one of the key obstacles which hinder the widely applications of high-order schemes for complex grid problems. In order to use high-order schemes for low quality grids, a conservative metric method (CMM) which can ensure the SCL has been derived by Deng et al [100]. The CMM contains the following two aspects:…”

Section: Geometric Conservative Law and The Conservative Metric Methodsmentioning

confidence: 99%

“…5(a). The flows conditions is set to be the same as that of [100], namely, Ma = 0.3, Re = 2.7×10 6 (base on the height of one step), and T ∞ = 300K. The solid wall is assumed to be adiabatic.…”

Section: The Gcl For a Blunt Configurationmentioning

confidence: 99%

“…The errors shown in Table 3 are larger than that in Table 1. We note here that the traditional standard metrics are referred as followings Our previous study shows that high-order traditional standard metric methods (CC6, [100]) may cause numerical oscillations when we conduct high-order flow computing. In this paper, we can find that the oscillations are still obvious (Fig.…”

Section: The Gcl For a Blunt Configurationmentioning

confidence: 99%

“…Deng et al have developed compact nonlinear schemes [8] and weighted compact nonlinear schemes (WCNS) [9,10]. The WCNSs have been successfully applied to a wide range of flow simulations so far to show its flexibility and robustness [11,16,32,99,100]. Some results on using the fifth-order WCNS (WCNS-E-5) [9,10] for complex grid problems are presented in this paper to further show its engineering prospects.…”

Section: Introductionmentioning

confidence: 99%

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

Deng

Mao

et al. 2012

Commun. comput. phys.

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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.

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

confidence: 99%

Section: Geometric Conservative Law and The Conservative Metric Methodsmentioning

confidence: 99%

Section: The Gcl For a Blunt Configurationmentioning

confidence: 99%

Section: The Gcl For a Blunt Configurationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Deng

Mao

et al. 2012

Commun. comput. phys.

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Developing a hybrid flux function suitable for hypersonic flow simulation with high‐order methods

Wang

Deng

Wang

et al. 2015

Numerical Methods in Fluids

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SUMMARYIn this paper, we develop a new hybrid Euler flux function based on Roe's flux difference scheme, which is free from shock instability and still preserves the accuracy and efficiency of Roe's flux scheme. For computational cost, only 5% extra CPU time is required compared with Roe's FDS. In hypersonic flow simulation with high-order methods, the hybrid flux function would automatically switch to the Rusanov flux function near shock waves to improve the robustness, and in smooth regions, Roe's FDS would be recovered so that the advantages of high-order methods can be maintained. Multidimensional dissipation is introduced to eliminate the adverse effects caused by flux function switching and further enhance the robustness of shock-capturing, especially when the shock waves are not aligned with grids. A series of tests shows that this new hybrid flux function with a high-order weighted compact nonlinear scheme is not only robust for shock-capturing but also accurate for hypersonic heat transfer prediction.

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A revised WENO‐THINC scheme for the general structured mesh and applications in the direct numerical simulation of compressible turbulent flows

Liu

2023

Numerical Methods in Fluids

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The Tangent of Hyperbola for INterface Capturing (THINC) scheme allows a jump‐like reconstruction and brings about a significant improvement in resolving the discontinuous part of the numerical solutions. However, it is found that the original THINC scheme loses accuracy when working on the stretched, curvilinear or highly‐skewed grid. In this study, we propose a simple strategy to determine the jump thickness parameter in the THINC function, so as to effectively suppress the unphysical oscillation. A Boundary Variation Diminishing (BVD) guideline is introduced to make options between the Weighted Essentially Non‐Oscillatory (WENO) scheme and the modified THINC scheme, thus both the smooth and discontinuous solutions can be reconstructed properly avoiding distortion of grids. Numerical validations indicate that the improved WENO‐THINC‐BVD approach maintains high resolution and is more robust on various types of non‐uniform meshes. The present method is further extended to validate the low‐dissipation property in resolving higher wave numbers portions by simulating an isotropic turbulence decay problem. Finally, we perform the direct numerical simulation (DNS) of a spatially evolving adiabatic flat plate boundary‐layer flow problem at a supersonic Mach number (). Numerical results show the predicted mean flow variables and the normalized shear stress agree well with the experimental data, significant improvements are found in the resolution of the small‐scale vortices, especially in the transition process.

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Geometric conservation law and applications to high-order finite difference schemes with stationary grids

Cited by 140 publications

References 38 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

Developing a hybrid flux function suitable for hypersonic flow simulation with high‐order methods

A revised WENO‐THINC scheme for the general structured mesh and applications in the direct numerical simulation of compressible turbulent flows

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