scholarly journals Numerical Simulation of Dam Break Flows Using a Radial Basis Function Meshless Method with Artificial Viscosity

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Elmiloud Chaabelasri
Keyword(s):  
Differential Equation ◽  
Radial Basis Function ◽  
Basis Function ◽  
Meshless Method ◽  
Artificial Viscosity ◽  
Dam Break ◽  
Two Dimensional ◽  
Radial Basis ◽  
Temporal Derivative ◽  
Irregular Bed Topography

A simple radial basis function (RBF) meshless method is used to solve the two-dimensional shallow water equations (SWEs) for simulation of dam break flows over irregular, frictional topography involving wetting and drying. At first, we construct the RBF interpolation corresponding to space derivative operators. Next, we obtain numerical schemes to solve the SWEs, by using the gradient of the interpolant to approximate the spatial derivative of the differential equation and a third-order explicit Runge–Kutta scheme to approximate the temporal derivative of the differential equation. For the problems involving shock or discontinuity solutions, we use an artificial viscosity for shock capturing. Then, we apply our scheme for several theoretical two-dimensional numerical experiments involving dam break flows over nonuniform beds and moving wet-dry fronts over irregular bed topography. Promising results are obtained.

scholarly journals A Direct Meshless Method for Solving Two-Dimensional Second-Order Hyperbolic Telegraph Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Fuzhang Wang ◽  
Enran Hou
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Meshless Method ◽  
Space Variable ◽  
Second Order ◽  
Time Variable ◽  
Time Dependent ◽  
Two Dimensional ◽  
Radial Basis ◽  
Telegraph Equations

In this paper, a direct meshless method (DMM), which is based on the radial basis function, is developed to the numerical solution of the two-dimensional second-order hyperbolic telegraph equations. Since these hyperbolic telegraph equations are time dependent, we present two schemes for the basis functions from radial and nonradial aspects. The first scheme is fulfilled by considering time variable as normal space variable to construct an “isotropic” space-time radial basis function. The other scheme considered a realistic relationship between space variable and time variable which is not radial. The time-dependent variable is treated regularly during the whole solution process and the hyperbolic telegraph equations can be solved in a direct way. Numerical experiments performed with the proposed numerical scheme for several two-dimensional second-order hyperbolic telegraph equations are presented with some discussions, which show that the DMM solutions are converging very fast in comparison with the various existing numerical methods.

Application of radial basis function-based meshless method for torsional analysis of elliptical and bone shaped-irregular sections

2021 ◽  
pp. 146442072110534
Author(s):  
Ram Bilas Prasad ◽  
Jeeoot Singh ◽  
Karunesh Kumar Shukla
Keyword(s):  
Differential Equations ◽  
Radial Basis Function ◽  
Functionally Graded Material ◽  
Basis Function ◽  
Meshless Method ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Radial Basis ◽  
Graded Material ◽  
Torsional Analysis

This article presents a torsional analysis of solid elliptical, hollow circular, and actual bone sections of orthotropic and functionally graded material. The formulation of the governing equation is done using the Saint-Venant torsion theory. A classical power law is considered for the modelling of functionally graded material. Five different radial basis functions-based meshless methods are used for the discretization of the governing differential equations. MATLAB code is developed to solve the discretized partial differential equations. A convergence and validation study has been carried out to demonstrate the effectiveness and accuracy of the present method. Numerical examples for torsional rigidity and shear stresses are presented for circular, elliptical, and bone-shaped irregular sections made up of orthotropic and functionally graded materials. Finally, the proposed radial basis function-based meshless method is applied to the modelling and torsional analysis of an actual bone cross-section.

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