Perspective on the geometric conservation law and finite element methods for ALE simulations of incompressible flow

ítienne, S.; Garon, André; Pelletier, Dominique

doi:10.1016/j.jcp.2008.11.032

Cited by 76 publications

(68 citation statements)

References 40 publications

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“…However, it may not be true in discretized forms because of numerical errors. Even when low-order schemes are used,Étienne et al [86] showed that a numerical method satisfying the VCL will generally allow a much larger computational time step than its counterpart violating the VCL. To ensure the VCL, the volume conservation item is usually applied to calculate the time derivative of Jacobian following…”

Section: Geometric Conservative Law and The Conservative Metric Methodsmentioning

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: Geometric Conservative Law and The Conservative Metric Methodsmentioning

confidence: 99%

“…by many authors [78,86]. The errors in I x , I y and I z are usually related to grid quality, such as smoothness, uniformity, orthogonality, and stretch rate.…”

Section: Geometric Conservative Law and The Conservative Metric Methodsmentioning

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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“…However, it has also been applied with finite differences [135], conforming finite elements [24,56,58], discontinuous Galerkin methods [114] (space-time FE and DG methods automatically satisfy the GCL [141]), and residual distribution schemes [99]. The paper ofÉtienne, Garon and Pelletier [56] includes a useful summary of the literature in this area and highlights three increasingly challenging levels of compliance with the GCL within a formulation of a moving mesh algorithm.…”

Section: The Gcl Methodsmentioning

confidence: 99%

Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations

Baines

Hubbard

Jimack

2011

Commun. comput. phys.

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Abstract. This article describes a number of velocity-based moving mesh numerical methods for multidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.

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“…A desvantagem desta forma é que ela depende da escolha da discretização temporal e da velocidade da malha para que a GCL seja satisfeita. Mais especificamente, um esquema satisfaz a GCL, se a relação Outra forma de satisfazer a GCL na forma conservativa, apresentada em Étienne et al [22], é, em vez de usar a velocidade da malha para calcular o termo ∇ · v h (i.e., calcular explicitamente o divergente da velocidade da malha discretizada v h ), troca-se tal termo por outro usando a bem conhecida relação da mecânica do contínuo (ver, e.g., [41]) …”

Section: Discretização Temporalunclassified

“…Em todos os casos, foi obtida a solução exata (dentro da precisão de máquina), diferentemente do que é reportado em Étienne et al [22] (também para um escoamente de Couette), que obteve apenas convergência linear para o CN na mesma formulação adotada neste trabalho (formulação não conservativa), mas que também obteve solução exata com a formulação conservativa.…”

Section: Convergência Em Malha Dinâmica -Iunclassified

Métodos numéricos para escoamentos com linhas de contato dinâmicas

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Perspective on the geometric conservation law and finite element methods for ALE simulations of incompressible flow

Cited by 76 publications

References 40 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

Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations

Métodos numéricos para escoamentos com linhas de contato dinâmicas

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