scholarly journals Meshless and analytical solutions to the time-dependent advection-diffusion-reaction equation with variable coefficients and boundary conditions

2017 ◽  
Vol 49 ◽  
pp. 220-242 ◽  
Author(s):  
M. Gharib ◽  
M. Khezri ◽  
S.J. Foster
Keyword(s):  
Boundary Conditions ◽  
Analytical Solutions ◽  
Variable Coefficients ◽  
Time Dependent ◽  
Diffusion Reaction ◽  
Reaction Equation ◽  
Advection Diffusion

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

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Hamid Mesgarani ◽  
Mahya Kermani ◽  
Mostafa Abbaszadeh
Keyword(s):  
Method Of Lines ◽  
Variable Coefficients ◽  
Diffusion Reaction ◽  
Test Problems ◽  
Reaction Equation ◽  
Content Type ◽  
Interpolation Matrix ◽  
Advection Diffusion ◽  
The Method Of Lines ◽  
Nonlinear Advection

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.

scholarly journals Numerical Simulation of Oil Spill in Ocean

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Yong-Sik Cho ◽  
Tak-Kyeom Kim ◽  
Woochang Jeong ◽  
Taemin Ha
Keyword(s):  
Oil Spill ◽  
Shallow Water Equations ◽  
Dispersion Model ◽  
Coastal Environment ◽  
Diffusion Reaction ◽  
Reaction Equation ◽  
Advection Diffusion ◽  
Coastal Damage ◽  
Spilled Oil ◽  
Marine Environmental

The spreading of oil in an open ocean may cause serious damage to a marine environmental system. Thus, an accurate prediction of oil spill is very important to minimize coastal damage due to unexpected oil spill accident. The movement of oil may be represented with a numerical model that solves an advection-diffusion-reaction equation with a proper numerical scheme. In this study, the spilled oil dispersion model has been established in consideration of tide and tidal currents simultaneously. The velocity components in the advection-diffusion-reaction equation are obtained from the shallow-water equations. The accuracy of the model is verified by applying it to a simple but significant problem. The results produced by the model agree with corresponding analytical solutions and field-observed data. The model is then applied to predict the spreading of an oil spill in a real coastal environment.

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