A high-order flux reconstruction method with adaptive mesh refinement and artificial diffusivity on unstructured moving/deforming mesh for shock capturing

Yang, Jingjing; Zhang, Bin; Liang, Chunlei; Rong, Yongwu

doi:10.1016/j.compfluid.2016.03.025

Cited by 13 publications

(16 citation statements)

References 31 publications

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“…It is evident that AMR method accelerates the solver substantially by allocating computing resources to shock regions. It is consistent with our findings in Yang et al that more levels of refinement only result in slightly deviation from the ideal speedup slope (ideally, when cell counts reduce by 50 % , a 2× acceleration should happen). It is also of vital importance at isolating various types of discontinuity and accurately capture them.…”

Section: Numerical Resultssupporting

confidence: 93%

“…By following these conditions, we presented a remarkably efficient AMR method, which allows the grid undergoes dynamic motions. The speedup curve in Yang et al shows only slight deviation from the ideal one due to minimal inclusion of the cost of AMR overheads and nonconforming interfaces. Detailed analysis and gain of acceleration can also be found in that article.…”

Section: Methodsmentioning

confidence: 94%

“…The continuous flux

{boldG}_{i j}^{c}

and its derivative in η direction can be obtained with the same procedures. The procedures for inviscid and viscous flux discretization can be found in other studies …”

Section: Methodsmentioning

confidence: 99%

“…f s w = H (−∇· u ) is a Heaviside function that used as a switch to turn off unnecessary ABV in smooth regions. The overbar denotes a smoothing filter . In the context of FR method, the smoothing is achieved by as follows: (1) interpolate higher‐order discretization of solution variables onto lower order (second) space, (2) smooth out the solution at the cell interfaces by arithmetic averaging, and (3) interpolate back to the original order.…”

Section: Methodsmentioning

confidence: 99%

“…34,35 The AMR method used in this article inherits the merits of the tree-free, direct-addressing approach of our previous study. 36 The time needed for retrieving flow variables and neighboring information across multiple level of grids is negligible. The design of data structure is rooted in unstructured and adaptive grids.…”

Section: Introductionmentioning

confidence: 99%

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A high‐order flux reconstruction adaptive mesh refinement method for magnetohydrodynamics on unstructured grids

Yang

Liang

2017

Numerical Methods in Fluids

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Summary We report our recent development of the high‐order flux reconstruction adaptive mesh refinement (AMR) method for magnetohydrodynamics (MHD). The resulted framework features a shock‐capturing duo of AMR and artificial resistivity (AR), which can robustly capture shocks and rotational and contact discontinuities with a fraction of the cell counts that are usually required. In our previous paper, we have presented a shock‐capturing framework on hydrodynamic problems with artificial diffusivity and AMR. Our AMR approach features a tree‐free, direct‐addressing approach in retrieving data across multiple levels of refinement. In this article, we report an extension to MHD systems that retains the flexibility of using unstructured grids. The challenges due to complex shock structures and divergence‐free constraint of magnetic field are more difficult to deal with than those of hydrodynamic systems. The accuracy of our solver hinges on 2 properties to achieve high‐order accuracy on MHD systems: removing the divergence error thoroughly and resolving discontinuities accurately. A hyperbolic divergence cleaning method with multiple subiterations is used for the first task. This method drives away the divergence error and preserves conservative forms of the governing equations. The subiteration can be accelerated by absorbing a pseudo time step into the wave speed coefficient, therefore enjoys a relaxed CFL condition. The AMR method rallies multiple levels of refined cells around various shock discontinuities, and it coordinates with the AR method to obtain sharp shock profiles. The physically consistent AR method localizes discontinuities and damps the spurious oscillation arising in the curl of the magnetic field. The effectiveness of the AMR and AR combination is demonstrated to be much more powerful than simply adding AR on finer and finer mesh, since the AMR steeply reduces the required amount of AR and confines the added artificial diffusivity and resistivity to a narrower and narrower region. We are able to verify the designed high‐order accuracy in space by using smooth flow test problems on unstructured grids. The efficiency and robustness of this framework are fully demonstrated through a number of two‐dimensional nonsmooth ideal MHD tests. We also successfully demonstrate that the AMR method can help significantly save computational cost for the Orszag‐Tang vortex problem.

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Section: Numerical Resultssupporting

confidence: 93%

Section: Methodsmentioning

confidence: 94%

“…The continuous flux

{boldG}_{i j}^{c}

and its derivative in η direction can be obtained with the same procedures. The procedures for inviscid and viscous flux discretization can be found in other studies …”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A high‐order flux reconstruction adaptive mesh refinement method for magnetohydrodynamics on unstructured grids

Yang

Liang

2017

Numerical Methods in Fluids

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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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Simple and robust h-adaptive shock-capturing method for flux reconstruction framework

Huang

Jiang

Lou

et al. 2023

Chinese Journal of Aeronautics

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A high-order flux reconstruction method with adaptive mesh refinement and artificial diffusivity on unstructured moving/deforming mesh for shock capturing

Cited by 13 publications

References 31 publications

A high‐order flux reconstruction adaptive mesh refinement method for magnetohydrodynamics on unstructured grids

A high‐order flux reconstruction adaptive mesh refinement method for magnetohydrodynamics on unstructured grids

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

Simple and robust h-adaptive shock-capturing method for flux reconstruction framework

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