Numerical investigation on the transport equation in spherical coordinates via generalized moving least squares and moving kriging least squares approximations

Mohammadi, V.; Dehghan, Mehdi; Khodadadian, Amirreza; Wick, Thomas

doi:10.1007/s00366-019-00881-3

Cited by 18 publications

(11 citation statements)

References 56 publications

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“…Mavric and Sarler (2015) developed a local RBF collocation method for solving linear thermoelasticity in two dimensions. Mohammadi et al (2019) have presented new and simple numerical methods for solving the time-dependent transport equation on the sphere in spherical coordinates. Khodadadian and Heitzinger (2016) used a basis-adaptation method based on polynomial chaos expansion for the stochastic nonlinear Poisson-Boltzmann equation.…”

Section: Application Of Spd-rbf Methods Of Linesmentioning

confidence: 99%

Application of SPD-RBF method of lines for solving nonlinear advection–diffusion–reaction equation with variable coefficients

Mesgarani

Kermani

Abbaszadeh

2021

HFF

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Purpose The purpose of this study is to use the method of lines to solve the two-dimensional nonlinear advection–diffusion–reaction equation with variable coefficients. Design/methodology/approach The strictly positive definite radial basis functions collocation method together with the decomposition of the interpolation matrix is used to turn the problem into a system of nonlinear first-order differential equations. Then a numerical solution of this system is computed by changing in the classical fourth-order Runge–Kutta method as well. Findings Several test problems are provided to confirm the validity and efficiently of the proposed method. Originality/value For the first time, some famous examples are solved by using the proposed high-order technique.

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Section: Application Of Spd-rbf Methods Of Linesmentioning

confidence: 99%

Application of SPD-RBF method of lines for solving nonlinear advection–diffusion–reaction equation with variable coefficients

Mesgarani

Kermani

Abbaszadeh

2021

HFF

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“…A meshless numerical procedure using the interpolating element-free Galerkin method was developed [11] to check the unconditional stability and convergence of the numerical scheme. The numerical solution of transport equation in spherical coordinates based on generalized moving least squares and kriging least-squares approximations was studied in [12].…”

Section: Introductionmentioning

confidence: 99%

Boussinesq Model and CFD Simulations of Non-Linear Wave Diffraction by a Floating Vertical Cylinder

Mohapatra

Islam

Soares

2020

JMSE

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A mathematical model for the problem of wave diffraction by a floating fixed truncated vertical cylinder is formulated based on Boussinesq equations (BEs). Using Bessel functions in the velocity potentials, the mathematical problem is solved for second-order wave amplitudes by applying a perturbation technique and matching conditions. On the other hand, computational fluid dynamics (CFD) simulation results of normalized free surface elevations and wave heights are compared against experimental fluid data (EFD) and numerical data available in the literature. In order to check the fidelity and accuracy of the Boussinesq model (BM), the results of the second-order super-harmonic wave amplitude around the vertical cylinder are compared with CFD results. The comparison shows a good level of agreement between Boussinesq, CFD, EFD, and numerical data. In addition, wave forces and moments acting on the cylinder and the pressure distribution around the vertical cylinder are analyzed from CFD simulations. Based on analytical solutions, the effects of radius, wave number, water depth, and depth parameters at specific elevations on the second-order sub-harmonic wave amplitudes are analyzed.

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“…In Dehghan and Abbaszadeh (2016), Brusselator system in 2D spaces is solved numerically via local discontinuous Galerkin (LDG) and variational multiscale element free Galerkin (VMEFG) methods. The interested reader can refer to Abbaszadeh et al (2019), Khodadadian et al (2019) and Mohammadi et al (2019), where the other meshless techniques are developed for solving mathematical models arising in some branches of applied science.…”

Section: Introductionmentioning

confidence: 99%

The boundary knot method for the solution of two-dimensional advection reaction-diffusion and Brusselator equations

Dehghan

Mohammadi

2020

HFF

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Purpose This study aims to apply a numerical meshless method, namely, the boundary knot method (BKM) combined with the meshless analog equation method (MAEM) in space and use a semi-implicit scheme in time for finding a new numerical solution of the advection–reaction–diffusion and reaction–diffusion systems in two-dimensional spaces, which arise in biology. Design/methodology/approach First, the BKM is applied to approximate the spatial variables of the studied mathematical models. Then, this study derives fully discrete scheme of the studied models using a semi-implicit scheme based on Crank–Nicolson idea, which gives a linear system of algebraic equations with a non-square matrix per time step that is solved by the singular value decomposition. The proposed approach approximates the solution of a given partial differential equation using particular and homogeneous solutions and without considering the fundamental solutions of the proposed equations. Findings This study reports some numerical simulations for showing the ability of the presented technique in solving the studied mathematical models arising in biology. The obtained results by the developed numerical scheme are in good agreement with the results reported in the literature. Besides, a simulation of the proposed model is done on buttery shape domain in two-dimensional space. Originality/value This study develops the BKM combined with MAEM for solving the coupled systems of (advection) reaction–diffusion equations in two-dimensional spaces. Besides, it does not need the fundamental solution of the mathematical models studied here, which omits any difficulties.

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Numerical investigation on the transport equation in spherical coordinates via generalized moving least squares and moving kriging least squares approximations

Cited by 18 publications

References 56 publications

Application of SPD-RBF method of lines for solving nonlinear advection–diffusion–reaction equation with variable coefficients

Application of SPD-RBF method of lines for solving nonlinear advection–diffusion–reaction equation with variable coefficients

Boussinesq Model and CFD Simulations of Non-Linear Wave Diffraction by a Floating Vertical Cylinder

The boundary knot method for the solution of two-dimensional advection reaction-diffusion and Brusselator equations

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