Numerical solution of the three-dimensional advection–diffusion equation

2004 ◽  
Vol 150 (1) ◽  
pp. 5-19 ◽  
Author(s):  
Mehdi Dehghan
Keyword(s):  
Diffusion Equation ◽  
Numerical Solution ◽  
Three Dimensional ◽  
Advection Diffusion Equation ◽  
Advection Diffusion

scholarly journals NUMERICAL MODEL OF 3D MORPHODYNAMIC AFTER OFFSHORE NOURISHMENT

2011 ◽  
Vol 1 (32) ◽  
pp. 55 ◽  
Author(s):  
Masamitsu Kuroiwa ◽  
Yoko Shibutani ◽  
Yuhei Matsubara ◽  
Takayuki Kuchiishi ◽  
Mazen Abualtyef
Keyword(s):  
Numerical Model ◽  
Diffusion Equation ◽  
Suspended Sediment Concentration ◽  
Three Dimensional ◽  
Sediment Concentration ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Sand Material

A three-dimensional model of morphodynamics after offshore nourishment was developed. In the presented model, the 3D beach evolution model that is not only after nourishment but also taking into account the nourishment process of injected sand material. In order to consider the injected process of sand, the computation using the advection-diffusion equation for suspended sediment concentration was adapted in the model. The presented model was applied to an idealized beach with two groins in order to investigate the performance of the model, and then, the model was applied to a field observation result for shoreface nourishment carried out at the Egmond aan Zee in the Netherlands. Finally, the applicability of the presented model was discussed from the computed results.

An Analytical Methodology to Air Pollution Modelling in Atmosphere

2019 ◽  
Vol 396 ◽  
pp. 91-98 ◽  
Author(s):  
Régis S. Quadros ◽  
Glênio A. Gonçalves ◽  
Daniela Buske ◽  
Guilherme J. Weymar
Keyword(s):  
Analytical Solution ◽  
Diffusion Equation ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Numerical Inversion ◽  
Analytical Methodology ◽  
Air Pollution Modelling ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Using Data

This work presents an analytical solution for the transient three-dimensional advection-diffusion equation to simulate the dispersion of pollutants in the atmosphere. The solution of the advection-diffusion equation is obtained analytically using a combination of the methods of separation of variables and GILTT. The main advantage is that the presented solution avoids a numerical inversion carried out in previous works of the literature, being by this way a totally analytical solution, less than a summation truncation. Initial numerical simulations and statistical comparisons using data from the Copenhagen experiment are presented and prove the good performance of the model.

scholarly journals Time-Splitting Procedures for the Numerical Solution of the 2D Advection-Diffusion Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
A. R. Appadu ◽  
H. H. Gidey
Keyword(s):  
Diffusion Equation ◽  
Numerical Solution ◽  
Optimization Technique ◽  
Step Size ◽  
One Dimensional ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Optimal Value ◽  
Time Splitting ◽  
Dispersion And Dissipation Errors

We perform a spectral analysis of the dispersive and dissipative properties of two time-splitting procedures, namely, locally one-dimensional (LOD) Lax-Wendroff and LOD (1, 5) [9] for the numerical solution of the 2D advection-diffusion equation. We solve a 2D numerical experiment described by an advection-diffusion partial differential equation with specified initial and boundary conditions for which the exact solution is known. Some errors are computed, namely, the error rate with respect to theL1norm, dispersion and dissipation errors. Lastly, an optimization technique is implemented to find the optimal value of temporal step size that minimizes the dispersion error for both schemes when the spatial step is chosen as 0.025, and this is validated by numerical experiments.

scholarly journals SOLUÇÃO DA EQUAÇÃO DE ADVECÇÃO-DIFUSÃO TRIDIMENSIONAL PELO MÉTODO GIADMT PARA DOIS TERMOS DE CONTRAGRADIENTE

2016 ◽  
Vol 38 ◽  
pp. 53
Author(s):  
Karine Rui ◽  
Camila Pinto da Costa
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Equation ◽  
Turbulent Flow ◽  
Turbulent Diffusion ◽  
Three Dimensional ◽  
Turbulent Diffusion Coefficient ◽  
Advection Diffusion Equation ◽  
Advection Diffusion

In this work, we present the resolution of the three-dimensional stationary advection-diffusion equation, through the GIADMT technique, considering the nonlocal closure for turbulent flow, using two different parameterization for the countergradient, one proposal by Cuijpers e Holtslag (1998) and another proposed by Roberti et al. (2004). The concentration of pollutants is estimated and compared with the observed data in Copenhagen experiment using different parameterization for the vertical turbulent diffusion coefficient.

scholarly journals Numerical solution of advection-diffusion equation using finite difference schemes

2020 ◽  
Vol 55 (1) ◽  
pp. 15-22
Author(s):  
LS Andallah ◽  
MR Khatun
Keyword(s):  
Diffusion Equation ◽  
Numerical Solution ◽  
Numerical Scheme ◽  
Finite Difference Schemes ◽  
Qualitative Behavior ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Nicolson Scheme ◽  
And Diffusion ◽  
Crank Nicolson

This paper presents numerical simulation of one-dimensional advection-diffusion equation. We study the analytical solution of advection diffusion equation as an initial value problem in infinite space and realize the qualitative behavior of the solution in terms of advection and diffusion co-efficient. We obtain the numerical solution of this equation by using explicit centered difference scheme and Crank-Nicolson scheme for prescribed initial and boundary data. We implement the numerical scheme by developing a computer programming code and present the stability analysis of Crank-Nicolson scheme for ADE. For the validity test, we perform error estimation of the numerical scheme and presented the numerical features of rate of convergence graphically. The qualitative behavior of the ADE for different choice of the advection and diffusion co-efficient is verified. Finally, we estimate the pollutant in a river at different times and different points by using these numerical scheme. Bangladesh J. Sci. Ind. Res.55(1), 15-22, 2020

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