Time-accurate local time stepping method based on flux updating

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

doi:10.2514/3.12195

Cited by 20 publications

(9 citation statements)

References 10 publications

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“…Some of the previous algorithms [3,7] attempt to connect the elements at different time levels by using flux interpolation or extrapolation techniques. Zhang et al [2] used flux at the previous time level (frozen flux concept) during local time steps. These strategies either increase runtime (in case of flux interpolation) or may cause instability in high gradient flows (in case of frozen flux).…”

Section: Local Flux Flagged-local Time Stepping (Lff-lts) Algorithmmentioning

confidence: 99%

“…In LFF-LTS algorithm, both frozen flux and flux calculation concepts are utilized by using the ratio of the local time step to Dt min . Following the frozen flux procedure as suggested by Zhang et al [2] and further developed by Crossley et al [3], the 2Dt min criterion is used to flag elements as G 1 and G 2 as given by Eq. (18).…”

Section: Local Flux Flagged-local Time Stepping (Lff-lts) Algorithmmentioning

confidence: 99%

“…To obtain the information at the interface between the cells at different time levels, linear interpolation was used. Zhang et al [2] introduced a LTS algorithm based on flux updating (LTS1). The procedure is to perform a series of temporal updates in GTS algorithm, while using the flux values calculated at a previous time level where possible (frozen flux).…”

Section: Introductionmentioning

confidence: 99%

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A novel Local Time Stepping algorithm for shallow water flow simulation in the discontinuous Galerkin framework

Maleki

Khan

2016

Applied Mathematical Modelling

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a b s t r a c tThis paper introduces a generic and efficient Local Time Stepping (LTS) algorithm called Local Flux Flagged-Local Time Stepping (LFF-LTS). The applicability of LFF-LTS algorithm to the solution of shallow water flow equations, utilizing the discontinuous Galerkin finite element framework, is investigated for uniform and non-uniform meshes. The proposed algorithm can be incorporated in any numerical scheme using an explicit time integration scheme. The new scheme is developed by combining and modifying the two existing LTS algorithms, where the domain time step (maximum allowable time step within the domain based on the Courant-Friedrichs-Lewy condition) and the local time step for an element is determined such that the stability criterion is satisfied for all elements. Frozen flux approximation is used during the intermediate time step as the solution for each element is advanced to the domain time step. The algorithm is applied to idealized and practical shallow water flow problems with wet/dry and partially wet bed conditions, and its accuracy and efficiency are compared to the traditional Global Time Stepping (GTS) method. Results show that, with no loss of accuracy, the new LTS algorithm achieves 47-73% CPU time reduction when compared to the GTS method. The accuracy of the LFF-LTS and GTS algorithms are compared with analytical/measured data and found to be in good agreement. The LFF-LTS algorithm is compared with the two existing LTS schemes and found to be more efficient.

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Section: Local Flux Flagged-local Time Stepping (Lff-lts) Algorithmmentioning

confidence: 99%

Section: Local Flux Flagged-local Time Stepping (Lff-lts) Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A novel Local Time Stepping algorithm for shallow water flow simulation in the discontinuous Galerkin framework

Maleki

Khan

2016

Applied Mathematical Modelling

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“…Without resorting to implicit and timestep-splitting techniques, it can only be increased via spatial and/or temporal refinement of the numerical solution. As a result, a number of explicit multiple time-stepping (MTS) methods have been developed for hyperbolic conservation laws [6,7,10,15,35,38]. The common strategy is to use each cell's maximum stable timestep rather than the value limited by the global CFL condition.…”

Section: Introductionmentioning

confidence: 99%

A time-accurate explicit multi-scale technique for gas dynamics

Omelchenko

Karimabadi

2007

Journal of Computational Physics

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“…The basis of the procedure outlined by Zhang et al [20,21] is to perform a series of temporal updates in the usual fashion, i.e. following a GTS approach, but using the same 'frozen' ux value as calculated from a previous time level where possible.…”

Section: Local Time Stepping Using a Frozen Ux (Lts1)mentioning

confidence: 99%

Time accurate local time stepping for the unsteady shallow water equations

Crossley

Wright

2005

Int. J. Numer. Meth. Fluids

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SUMMARYTwo time accurate local time stepping (LTS) strategies originally developed for the Euler equations are presented and applied to the unsteady shallow water equations of open channel ow. Using the techniques presented allows individual cells to be advanced to di erent points in time, in a time accurate fashion. The methods shown are incorporated into an explicit ÿnite volume version of Roe's scheme which is implemented in conjunction with an upwind treatment for the source terms. A comparison is made between the results obtained using the conventional time stepping approach and the two LTS methods through a series of test cases. The results illustrate a number of beneÿts of using LTS which included reduced run times and improved solution accuracy. In addition it is shown how using an upwind source term treatment can be beneÿcial for ows dominated by the geometry.

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Time-accurate local time stepping method based on flux updating

Cited by 20 publications

References 10 publications

A novel Local Time Stepping algorithm for shallow water flow simulation in the discontinuous Galerkin framework

A novel Local Time Stepping algorithm for shallow water flow simulation in the discontinuous Galerkin framework

A time-accurate explicit multi-scale technique for gas dynamics

Time accurate local time stepping for the unsteady shallow water equations

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