An interface treating technique for compressible multi-medium flow with Runge–Kutta discontinuous Galerkin method

Wang, Chunwu; Shu, Chi-Wang

doi:10.1016/j.jcp.2010.08.012

Cited by 34 publications

(16 citation statements)

References 37 publications

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“…However the result of the fifth order method is in better agreement with the converged reference solution than the second order method, especially in the region with fine structures, on this relatively coarse mesh. This is similar to the results in [50].…”

Section: (83)supporting

confidence: 92%

“…Example 5 This example is used to demonstrate the advantage of high order methods as in [50] for two-medium flows. It contains both shocks and fine structures in smooth regions, which is a simple model for shock-turbulence interactions.…”

Section: (83)mentioning

confidence: 99%

“…[28][29][30]49] and the references therein. Later, these techniques are used to develop the Runge-Kutta discontinuous Galerkin (RKDG) finite element method for multi-medium flow in [36,37,50,55]. The GFM, even though approximating directly the conservative Euler equations, is in general not a conservative method because the flux at the interface is double-valued.…”

Section: Introductionmentioning

confidence: 99%

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WENO Scheme with Subcell Resolution for Computing Nonconservative Euler Equations with Applications to One-Dimensional Compressible Two-Medium Flows

2012

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High order path-conservative schemes have been developed for solving nonconservative hyperbolic systems in (Parés, SIAM this approach may have some computational issues and shortcomings. In this paper, a modification to the high order path-conservative scheme in (Castro et al., Math. Comput. 75:1103-1134, 2006) is proposed to improve its computational performance and to overcome some of the shortcomings. This modification is based on the high order finite volume WENO scheme with subcell resolution and it uses an exact Riemann solver to catch the right paths at the discontinuities. An application to one-dimensional compressible two-medium flows of nonconservative or primitive Euler equations is carried out to show the effectiveness of this new approach.

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Section: (83)supporting

confidence: 92%

Section: (83)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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WENO Scheme with Subcell Resolution for Computing Nonconservative Euler Equations with Applications to One-Dimensional Compressible Two-Medium Flows

2012

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“…This example is used to demonstrate the advantage of high order methods as in [47] We can find that the two methods can both capture the correct solution, however the result of the fifth order method is in better agreement with the converged reference solution than the second order method, especially in the region with fine structures, on this relatively coarse mesh. This is is similar to the results in [47].…”

Section: Examplementioning

confidence: 93%

“…[25,26,27,46] and the references therein. Later, these techniques are used to develop the Runge-Kutta discontinuous Galerkin (RKDG) finite element method for multi-medium flow in [33,34,51,47]. The GFM, even though approximating directly the conservative Euler equations, is in general not a conservative method because the flux at the interface is double-valued.…”

Section: Introductionmentioning

confidence: 99%

WENO Scheme with Subcell Resolution for Computing Nonconservative Euler Equations with Applications to One-dimensional Compressible Two-medium Flows

Xiong¹,

Shu²,

Zhang³

2011

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High order path-conservative schemes have been developed for solving nonconservative hyperbolic systems in [32,7,6]. Recently, it has been observed in [3] that this approach may have some computational issues and shortcomings. In this paper, a modification to the high order path-conservative scheme in [7], based on the high order finite volume WENO scheme with subcell resolution and utilizing the exact Riemann solver to catch the right paths at the discontinuities, is proposed to improve its computational performance and to overcome some of the shortcomings. An application to one-dimensional compressible two-medium flows of nonconservative or primitive Euler equations is carried out to show the effectiveness of this new approach. Keywords

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Modified ghost fluid method for three‐dimensional compressible multimaterial flows with interfaces exhibiting large curvature and topological change

Liu

2020

Numerical Methods in Fluids

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Summary In order to capture the material interface dynamics, especially under the impact of strong shocks, the key feature of the modified ghost fluid method (MGFM) is to construct a multimaterial Riemann problem normal to the interface and use its solution to define interface conditions. However, such process sometimes may not be easily or accurately implemented when the multidimensional interfaces come into contact or undergo significant deformations. In this article, a three‐dimensional interface treating procedure is developed for a wide range of compressible multimaterial flows. It utilizes the MGFM with an explicit approximate Riemann problem solver to define interface conditions. More importantly, a weighted average technique is designed to optimize the treatment for interfaces exhibiting large curvature and topological change. This remedies two defects of the traditional approach in these extreme cases. One is that the normal directions of interfacial ghost nodes may not be easily calculated. The other is that the interface conditions may not be accurately defined. The numerical methodology is validated through several typical problems, including gas‐liquid Riemann problem and shock‐bubble/droplet interaction. These results indicate that the developed method is capable of dealing with interfacial evolutions in three dimensions, especially when interfaces undergo merger, fragmentation, and other complex changes.

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An interface treating technique for compressible multi-medium flow with Runge–Kutta discontinuous Galerkin method

Cited by 34 publications

References 37 publications

WENO Scheme with Subcell Resolution for Computing Nonconservative Euler Equations with Applications to One-Dimensional Compressible Two-Medium Flows

WENO Scheme with Subcell Resolution for Computing Nonconservative Euler Equations with Applications to One-Dimensional Compressible Two-Medium Flows

WENO Scheme with Subcell Resolution for Computing Nonconservative Euler Equations with Applications to One-dimensional Compressible Two-medium Flows

Modified ghost fluid method for three‐dimensional compressible multimaterial flows with interfaces exhibiting large curvature and topological change

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