Convergence of Finite Element Lax-Wendroff Method for Linear Hyperbolic Differential Equation

Kawahara, Mutsuto

doi:10.2208/jscej1969.1976.253_95

Cited by 7 publications

(3 citation statements)

References 10 publications

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“…For the time discretization, the two-step scheme of LaxWendroff is applied (Kawahara, 1976;Kawahara et al, 1982;1984). From the equations, the unknown variables can be solved simultaneously.…”

Section: Finite Element Formulationmentioning

confidence: 99%

Numerical Analysis of Flow Pattern by Outflow Gates with Manifold Channel

Kim¹,

Changlym²,

Ku³

et al. 2011

Journal of Korean Society of Coastal and Ocean Engineers

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: For the improvement of water quality in a harbor, several studies have been carried out on SEB (Seawater Exchange Breakwater) in recent years, but a problem has been shown whereby the water on the inside area far from the SEB cannot be easily exchanged. In order to solve the problem of the SEB, the Manifold channel, a new concept of the SEB, is introduced in this paper. By using the manifold channel, it is possible to exchange the water of the inside area for seawater from the outside. Here, to assess the outflow gates of the manifold channel governing flow behavior, a virtual manifold channel controlled the location, width and direction of outflow gates applied to the Jumunjin fishery port, where the SEB has been established. In addition, the desirable flow pattern of the port by utilizing the two layer current model is identified, and five general cases of the manifold channel are described in this paper. The model is verified by comparing with observation of the SEB model, and the results are in general agreement. From the results of the manifold channel, in the case of the Jumunjin fishery port, the small circulation of counter clockwise is necessary for the water exchange on the inside area, but it should be controlled by the outflow gates for other areas. Using the two layer current model, the desirable flow pattern of the port can be predicted, and the water exchange for the upper and lower layer can be examined. For the practical use of the manifold channel, further studies on the manifold channel will be necessary, and it may then be used broadly for the design of breakwater in the future.

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Section: Finite Element Formulationmentioning

confidence: 99%

Numerical Analysis of Flow Pattern by Outflow Gates with Manifold Channel

Kim¹,

Changlym²,

Ku³

et al. 2011

Journal of Korean Society of Coastal and Ocean Engineers

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show abstract

“…The upwind methods can suppress the oscillations, but the artificial diffusion may be intolerable. In the present calculation, the second-order Taylor-Galerkin finite element method (Kawahara, 1976;Donea, 1984, Lohner et al, 1984 is used. Expanding in a Taylor series in time about t = t", the intermediate velocity value Vi can be expressed as…”

Section: The Convection Phasementioning

confidence: 99%

“…This method is based on the Lax-Wendroff finite difference method. In 1976, the finite element Lax-Wendroff method was proposed by Kawahara (1976) for linear convection equation. By exploiting the Taylor series expansion in the time discretization up to the third order before performing the Galerkin spatial discretization, the Taylor-Galerkin finite element method was proposed (Donea, 1984;Selmin, 1985) for the hyperbolic equation.…”

Section: Introductionmentioning

confidence: 99%

A Taylor–Galerkin-based finite element method for turbulent flows

Jiang¹,

Kawahara²,

Kashiyama³

1992

Fluid Dyn. Res.

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A finite element method is applied to solve the two-dimensional turbulent channel flows. Based on the fractional step techniques, the momentum and the k -€ equations arc split into convection and diffusion equations. The convection equations are solved by the second-order Taylor-Galerkin finite element method, which can overcome the spurious oscillations with minimal artificial diffusion, and the diffusion equations are solved by the fully explicit Galerkin method. Since the same order interpolation is used for the velocity, pressure and turbulent quantities, the present method is computationally efficient. The sudden expansion flow and the obstructed turbulent channel flow arc studied. The results arc in good agreement with experimental observations.

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A finite element method for high Reynolds number viscous fluid flow using two step explicit scheme

Kawahara

Hirano

1983

Numerical Methods in Fluids

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SUMMARYThis paper presents the finite element method for the analysis of unsteady viscous flow of fluid at high Reynolds numbers. The method is based on the explicit numerical integration scheme in time and uses three node triangular finite elements. For the convenience of the formulation, slight compressibility is considered. For the explicit scheme, the selective lumping two step scheme has been successfully employed. Vortex shedding behind a cylinder has been computed and compared with the conventional experimental results. The results agree favourably when both schemes are compared.

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Convergence of Finite Element Lax-Wendroff Method for Linear Hyperbolic Differential Equation

Cited by 7 publications

References 10 publications

Numerical Analysis of Flow Pattern by Outflow Gates with Manifold Channel

Numerical Analysis of Flow Pattern by Outflow Gates with Manifold Channel

A Taylor–Galerkin-based finite element method for turbulent flows

A finite element method for high Reynolds number viscous fluid flow using two step explicit scheme

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