Generalized finite difference method for two-dimensional shallow water equations

Li, Po-Wei; Fan, Chia‐Ming

doi:10.1016/j.enganabound.2017.03.012

Cited by 93 publications

(15 citation statements)

References 29 publications

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“…Recently, Generalized FDM (GFDM) is developed, and Li and Liu [6] proposed the main objective of the GFDM method is to approximate the spatial derivatives of a differentiable function in terms of its values at some randomly distributed nodes. GFDM uses meshless methods and thus suitable for any geometry of the domain and has been used to solve, 2-D shallow water equations [7], sloshing phenomena in a wave tank [8], the Poisson's equation on irregular 2D domains [9] etc.…”

Section: 1mentioning

confidence: 99%

Thermal Hydraulic Analysis of Multi-pass Heat Exchanger using a FDM Based Network Model

Samantara¹,

Sarathy²,

Kasinathan³

et al. 2019

JEES

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In order to analyze the performance of a multi-pass shell and tube type heat exchanger used for decay heat removal operation in fast breeder reactor, a computer code has been developed using network model. The model is based on 1-D finite difference method (FDM) formulations. The transient momentum and continuity equations are solved simultaneously to obtain pressure field and flow rates, viz., inlet flow over a distributed inlet window, cross flow between radial zones, and axial flows along the length. Intermixing between radial zones is modeled using cross flow. Transient energy equation is solved to obtain temperatures. The heat transfer capacity of the heat exchanger is estimated as 8.93 MW when the hot pool is at 547 °C. Natural circulation flow rate of primary sodium is found to be 46.3 kg/s. The results are compared with the CFD results and a reasonable agreement is found. A transient study is also carried out and the results are given in this paper.

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Section: 1mentioning

confidence: 99%

Thermal Hydraulic Analysis of Multi-pass Heat Exchanger using a FDM Based Network Model

Samantara¹,

Sarathy²,

Kasinathan³

et al. 2019

JEES

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“…The earliest numerical methods for wave equations include the finite difference method [8], the finite element method [9], the boundary element method [10] and the finite volume method [11]. It should be noted that most of the existed numerical methods are still based on the finite difference method (FDM) [12,13], which lead to two-step finite difference approximations.…”

Section: Introductionmentioning

confidence: 99%

A Novel Meshfree Strategy for a Viscous Wave Equation With Variable Coefficients

et al. 2021

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A one-step new general mesh free scheme, which is based on radial basis functions, is presented for a viscous wave equation with variable coefficients. By constructing a simple extended radial basis function, it can be directly applied to wave propagation by using the strong form-based mesh free collocation method. There is no need to deal with the time-dependent variable particularly. Numerical results for a viscous wave equation with variable coefficients show that the proposed mesh free collocation method is simple with accurate solutions.

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“…Nowadays, some of the most recent advances include: computational acoustics (Wei et al, 2015), the solution of nonlinear water waves using potential flow theory (Zhang et al, 2016 andFan et al, 2018), application to bidimensional shallow water equations (Li and Fan, 2017) and tridimensional adaptive cloud refinement (Gavete et al, 2018). As described by Zhang et al (2016), the GFDM is versatile enough for many engineering applications.…”

Section: Introductionmentioning

confidence: 99%

Reduced-order strategy for meshless solution of plate bending problems with the generalized finite difference method

Ferreira

Ribeiro

2019

Lat. Am. j. solids struct.

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This paper presents some recent advances on the numerical solution of the classical Germain-Lagrange equation for plate bending of thin elastic plates. A meshless strategy using the Generalized Finite Difference Method (GFDM) is proposed upon substitution of the original fourth-order differential equation by a system composed of two second-order partial differential equations. Mixed boundary conditions, variable nodal density and curved contours are some of the explored aspects. Simulations using very dense clouds and parallel processing scheme for efficient neighbor selection are also presented. Numerical experiments are performed for arbitrary plates and compared with analytical and Finite Element Method solutions. Finally, an overview of the procedure is presented, including a discussion of some future development.

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Generalized finite difference method for two-dimensional shallow water equations

Cited by 93 publications

References 29 publications

Thermal Hydraulic Analysis of Multi-pass Heat Exchanger using a FDM Based Network Model

Thermal Hydraulic Analysis of Multi-pass Heat Exchanger using a FDM Based Network Model

A Novel Meshfree Strategy for a Viscous Wave Equation With Variable Coefficients

Reduced-order strategy for meshless solution of plate bending problems with the generalized finite difference method

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