High-Order Overset Flux Reconstruction Method for Dynamic Moving Grids

Duan, Zhaowen; Wang, Z. J.

doi:10.2514/1.j059185

Cited by 7 publications

(3 citation statements)

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“…The radial (σ rr ) and hoop (σ θθ ) stresses are σ rr (r ) = λ( rr + θθ ) + 2μ rr , σ θθ (r ) = λ( rr + θθ ) + 2μ θθ , (29) where (λ, μ) ∈ {(λ 1 , μ 1 ), (λ 2 , μ 2 )}. The shear stress is zero everywhere.…”

Section: Bimaterials Diskmentioning

confidence: 99%

“…It is worth mentioning that there exist several methods that IBCM shares the essential idea with. First, a popular group of methods in computational fluid dynamics, called overset grid methods [24][25][26][27][28][29], also employ boundary-fitted meshes near geometric features while keeping discretization simple elsewhere. However, the two methods differ in the key building blocks such as geometric representations and treatment of coupling interfaces.…”

Section: Introductionmentioning

confidence: 99%

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Immersed boundary-conformal isogeometric method for linear elliptic problems

et al. 2021

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We present a novel isogeometric method, namely the Immersed Boundary-Conformal Method (IBCM), that features a layer of discretization conformal to the boundary while employing a simple background mesh for the remaining domain. In this manner, we leverage the geometric flexibility of the immersed boundary method with the advantages of a conformal discretization, such as intuitive control of mesh resolution around the boundary, higher accuracy per degree of freedom, automatic satisfaction of interface kinematic conditions, and the ability to strongly impose Dirichlet boundary conditions. In the proposed method, starting with a boundary representation of a geometric model, we extrude it to obtain a corresponding conformal layer. Next, a given background B-spline mesh is cut with the conformal layer, leading to two disconnected regions: an exterior region and an interior region. Depending on the problem of interest, one of the two regions is selected to be coupled with the conformal layer through Nitsche’s method. Such a construction involves Boolean operations such as difference and union, which therefore require proper stabilization to deal with arbitrarily cut elements. In this regard, we follow our precedent work called the minimal stabilization method (Antolin et al in SIAM J Sci Comput 43(1):A330–A354, 2021). In the end, we solve several 2D benchmark problems to demonstrate improved accuracy and expected convergence with IBCM. Two applications that involve complex geometries are also studied to show the potential of IBCM, including a spanner model and a fiber-reinforced composite model. Moreover, we demonstrate the effectiveness of IBCM in an application that exhibits boundary-layer phenomena.

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Section: Bimaterials Diskmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Immersed boundary-conformal isogeometric method for linear elliptic problems

et al. 2021

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“…14,15 According to the property of different parameters, some optimization works have been done. 16 Also, FR scheme has been applied in real applications like large-eddy simulation (LES), 17 overset grid, 18 multi-phase simulations, 19,20 and so forth.…”

Section: Introductionmentioning

confidence: 99%

Shock capturing with the high‐order flux reconstruction method on adaptive meshes based on p4est

Xia

2022

Engineering Reports

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High order schemes have been investigated for quite a long time, and the flux reconstruction (FR) scheme proposed by Huynh recently attracts the attention of researchers due to its simplicity and efficiency. Building the framework that bridges discontinuous Galerkin (DG) and spectral difference (SD) schemes, FR recovers DG and SD conveniently with a careful selection of parameters. In this article, FR scheme is realized based on the framework of p4est, an open source adaptive mesh refinement library. The shock capturing ability of localized Laplacian artificial viscosity and in‐cell piecewise integrated solution methods are compared. Curved boundary treatment for high order schemes is adopted. The performance of developed code is estimated in both one and two dimensions including curved boundary and shock cases, and some attractive results are obtained.

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