A high order ENO conservative Lagrangian type scheme for the compressible Euler equations

Cheng, Juan; Shu, Chi‐Wang

doi:10.1016/j.jcp.2007.09.017

Cited by 138 publications

(163 citation statements)

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“…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.

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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%

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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“…One of the key ingredients in ICF simulation is the ability to preserve symmetries. While this goal is not reached in [6], we achieve it in this paper. (2) We also want to examine the behavior of ENO-like reconstruction for Glace/Chic schemes.…”

Section: Introductionmentioning

confidence: 91%

“…Then, P.-H. Maire et al modified Glace's flux computation to build the Chic scheme which is more stable but more dissipative [9]. Alternatively, J. Cheng and C.-W. Shu published a new semi-Lagrangian scheme based on ENO reconstruction [6].…”

Section: Introductionmentioning

confidence: 99%

“…Récemment, des alternatives intéressantes au schéma historique VNR [15] ontété proposées dans [7] puis dans [9]. Parallèlement, un schéma WENO aété proposé dans [6]. Ce schéma ne préserve pas les symétries et le calcul des vitesses peutêtre discuté.…”

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“…These two first order schemes are multidimensional generalizations of the Godunov acoustic solver. Alternatively, a WENO Lagrangian scheme was proposed in [6]. This scheme suffers from non-preservation of symmetries and its velocity computation can be discussed.…”

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Polynomial Least-Squares reconstruction for semi-Lagrangian Cell-Centered Hydrodynamic Schemes

et al. 2009

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Abstract. In Inertial Confinement Fusion (ICF) simulation, use of Lagrangian hydrodynamic numerical schemes is a cornerstone. It avoids mixing of materials and allows for symmetry preservation in dimension two. Recently, [7] and then [9] proposed an interesting alternative to the historical VNR scheme [15]. These two first order schemes are multidimensional generalizations of the Godunov acoustic solver. Alternatively, a WENO Lagrangian scheme was proposed in [6]. This scheme suffers from non-preservation of symmetries and its velocity computation can be discussed.The aim of this work is to evaluate the later scheme on ICF representative test cases and to derive a polynomial reconstruction that preserves symmetries for the three cell-centered scheme. This reconstruction is inspired by [12]. Since this paper focuses on the approximation of Euler equations, considered test cases are purely hydrodynamic and do not illustrate all difficulties encountered in ICF.We first briefly recall different schemes used for this study. We then explain the Least-Squares ENO reconstruction that we chose for symmetry preservation and describe the limiting strategy. We finally illustrates the presented results by some representative numerical experiments.Résumé. La simulation de Fusion par Confinement Inertiel (FCI) utilise souvent des schémas hydrodynamiques Lagrangiens. Cela permet d'éviter le mélange de matériaux et permet de préserver des symétries en dimension deux. Récemment, des alternatives intéressantes au schéma historique VNR [15] ontété proposées dans [7] puis dans [9]. Parallèlement, un schéma WENO aété proposé dans [6]. Ce schéma ne préserve pas les symétries et le calcul des vitesses peutêtre discuté. L'objectif de ce travail est d'évaluer ce dernier schéma pour des cas tests représentatifs de la FCI et d'écrire une reconstruction polynomiale qui préserve les symétries pour les trois schémasétudiés. Cette reconstruction est inspirée de [12]. Puisqu'on se concentre ici sur la résolution deséquations d'Euler, les cas tests présentés sont purement hydrodynamiques et ne prétendent pas couvrir l'ensemble des difficultés rencontrées en FCI.Nous rappelons d'abord les différents schémas utilisés ici. Nous expliquons ensuite la reconstruction au sens des moindres carrés que nous avons choisie ainsi qu'une stratégie de limitation préservant aussi la symétrie. On illustre finalement les résultats au travers de quelques cas tests représentatifs choisis.

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A moving mesh BGK scheme for multi‐material flows

Jiang

2011

Numerical Methods in Fluids

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SUMMARY In this paper, a moving mesh BGK scheme (MMBGK) for multi‐material flow computations is proposed. The basic idea of constructing the MMBGK is to couple the Lagrangian method, which tracks material interfaces and keeps the interfaces sharp, with a remapping‐free ALE‐type kinetic method within each single material region, where the kinetic method is based on the BGK (Bhatnagar–Gross–Krook) model. Within each single material region, a numerical flux formulation is developed on moving meshes from motion of microscope particles, and the mesh velocity is determined by requiring both mesh adaptation for accuracy and robustness, such that the grids are moving towards to the regions with high flow gradients in a way of diffusive mechanism (velocity) to adjust the distances between neighboring cells, thus increasing the numerical accuracy. To keep the sharpness of material interfaces, the Lagrangian velocity and flux are constructed at the interfaces only. Consequently, a BGK‐scheme‐based ALE‐type method (i.e., the MMBGK scheme) for multi‐material flows is constructed. Numerical examples in one and two dimensions are presented to illustrate the accuracy and robustness of the MMBGK scheme. Copyright © 2011 John Wiley & Sons, Ltd.

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A high order ENO conservative Lagrangian type scheme for the compressible Euler equations

Cited by 138 publications

References 39 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

Polynomial Least-Squares reconstruction for semi-Lagrangian Cell-Centered Hydrodynamic Schemes

A moving mesh BGK scheme for multi‐material flows

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