Discrete form of the GCL for moving meshes and its implementation in CFD schemes

Zhang, H.; Reggio, Marcelo; Trépanier, Jean‐Yves; Camarero, R.

doi:10.1016/0045-7930(93)90003-r

Cited by 126 publications

(81 citation statements)

References 21 publications

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“…The GCL usually is divided into the volume conservation law (VCL) and the surface conservation law (SCL) as discussed by Zhang et al [93]. In fact, I t = I x = I y = I z = 0 analytically provided that the grids are differentiable.…”

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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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%

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, many obstacles prevent this condition from being fulfilled in a straightforward fashion. First, it seems particularly attractive to split the GCL in separate parts for each face of the control volume as was shown in previous work for time-marching methods [87,93]. In fact, the exact volume of the cell is known at all time instances since it is only a function of the position of the cell vertices, which is known from the mesh deformation algorithm.…”

Section: Applying the Spatial Discretization Equation (421) Is Exprmentioning

confidence: 99%

Three-Dimensional Aeroelastic Solutions via the Nonlinear Frequency-Domain Method

Tardif

Nadarajah

2017

AIAA Journal

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“…In the case of non-vanishing grid velocity the CFL-condition for the convective term reads (cf. [9])…”

Section: The Extended Projection Methodsmentioning

confidence: 99%

“…In [21] and [9] the GCL is used to compute the grid velocities from the grid node positions at different times. Thus, the GCL is automatically satisfied by the discretization scheme.…”

Section: Discretization Of the Geometric Conservation Lawmentioning

confidence: 99%

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Flow simulation on moving boundary-fitted grids and application to fluid-structure interaction problems

Engel

Griebel

2005

Int. J. Numer. Meth. Fluids

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SUMMARYWe present a method for the parallel numerical simulation of transient three-dimensional fluidstructure interaction problems. Here, we consider the interaction of incompressible flow in the fluid domain and linear elastic deformation in the solid domain. The coupled problem is tackled by an approach based on the classical alternating Schwarz method with non-overlapping subdomains, the subproblems are solved alternatingly and the coupling conditions are realized via the exchange of boundary conditions. The elasticity problem is solved by a standard linear finite element method. A main issue is that the flow solver has to be able to handle time-dependent domains. To this end, we present a technique to solve the incompressible Navier-Stokes equation in three-dimensional domains with moving boundaries. This numerical method is a generalization of a finite volume discretization using curvilinear coordinates to time-dependent coordinate transformations. It corresponds to a discretization of the Arbitrary Lagrangian-Eulerian formulation of the Navier-Stokes equations. Here the grid velocity is treated in such a way that the so-called Geometric Conservation Law is implicitly satisfied. Altogether, our approach results in a scheme which is an extension of the well-known MACmethod to a staggered mesh in moving boundary-fitted coordinates which uses grid-dependent velocity components as the primary variables.To validate our method, we present some numerical results which show that second order convergence in space is obtained on moving grids. Finally, we give the results of a fully coupled fluidstructure interaction problem. It turns out that already a simple explicit coupling with one iteration of the Schwarz method, i.e. one solution of the fluid problem and one solution of the elasticity problem per time step, yields a convergent, simple, yet efficient overall method for fluid-structure interaction problems.

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Discrete form of the GCL for moving meshes and its implementation in CFD schemes

Cited by 126 publications

References 21 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

Three-Dimensional Aeroelastic Solutions via the Nonlinear Frequency-Domain Method

Flow simulation on moving boundary-fitted grids and application to fluid-structure interaction problems

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