scholarly journals Numerical Solutions of Unsteady Advection-Diffusion Equations by Using EG Iteration with Wave Variable Transformation

2019 ◽  
Vol 1358 ◽  
pp. 012049
Author(s):  
Nur Afza Mat Ali ◽  
Rostang Rahman ◽  
Jumat Sulaiman ◽  
Khadizah Ghazali
Keyword(s):  
Numerical Solutions ◽  
Diffusion Equations ◽  
Variable Transformation ◽  
Wave Variable ◽  
Advection Diffusion

An efficient Bi-cubic B-spline ADI method for numerical solutions of two-dimensional unsteady advection diffusion equations

2018 ◽  
Vol 28 (11) ◽  
pp. 2620-2649 ◽  
Author(s):  
Rajni Rohila ◽  
R.C. Mittal
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Diffusion Equations ◽  
Spline Functions ◽  
Two Dimensional ◽  
Partial Differential ◽  
Content Type ◽  
B Spline ◽  
Advection Diffusion

Purpose This paper aims to develop a novel numerical method based on bi-cubic B-spline functions and alternating direction (ADI) scheme to study numerical solutions of advection diffusion equation. The method captures important properties in the advection of fluids very efficiently. C.P.U. time has been shown to be very less as compared with other numerical schemes. Problems of great practical importance have been simulated through the proposed numerical scheme to test the efficiency and applicability of method. Design/methodology/approach A bi-cubic B-spline ADI method has been proposed to capture many complex properties in the advection of fluids. Findings Bi-cubic B-spline ADI technique to investigate numerical solutions of partial differential equations has been studied. Presented numerical procedure has been applied to important two-dimensional advection diffusion equations. Computed results are efficient and reliable, have been depicted by graphs and several contour forms and confirm the accuracy of the applied technique. Stability analysis has been performed by von Neumann method and the proposed method is shown to satisfy stability criteria unconditionally. In future, the authors aim to extend this study by applying more complex partial differential equations. Though the structure of the method seems to be little complex, the method has the advantage of using small processing time. Consequently, the method may be used to find solutions at higher time levels also. Originality/value ADI technique has never been applied with bi-cubic B-spline functions for numerical solutions of partial differential equations.

STABILITY AND ACCURACY OF LATTICE BOLTZMANN SCHEMES FOR ANISOTROPIC ADVECTION-DIFFUSION EQUATIONS

2009 ◽  
Vol 20 (04) ◽  
pp. 633-650 ◽  
Author(s):  
SHINSUKE SUGA
Keyword(s):  
Lattice Boltzmann ◽  
Numerical Experiments ◽  
Numerical Solutions ◽  
Velocity Model ◽  
Diffusion Equations ◽  
Benchmark Problems ◽  
Relaxation Parameters ◽  
Advection Diffusion ◽  
The Stability ◽  
Stability And Accuracy

The stability of the numerical schemes for anisotropic advection-diffusion equations derived from the lattice Boltzmann equation with the D2Q4 particle velocity model is analyzed through eigenvalue analysis of the amplification matrices of the scheme. Accuracy of the schemes is investigated by solving benchmark problems, and the LBM scheme is compared with traditional implicit schemes. Numerical experiments demonstrate that the LBM scheme produces stable numerical solutions close to the analytical solutions when the values of the relaxation parameters in x and y directions are greater than 1.9 and the Courant numbers satisfy the stability condition. Furthermore, the numerical solutions produced by the LBM scheme are more accurate than those of the Crank–Nicolson finite difference scheme for the case where the Courant numbers are set to be values close to the upper bound of the stability region of the scheme.

scholarly journals A finite Volume Runge-Kutta Ellam Method for the Solution of Advection Diffusion Equations

2001 ◽  
Vol 6 (2) ◽  
pp. 67 ◽  
Author(s):  
Mohammed Al-Lawatia ◽  
Robert C. Sharpley ◽  
Hong Wang
Keyword(s):  
Contaminant Transport ◽  
Finite Volume ◽  
Large Time ◽  
Numerical Solutions ◽  
Standard Test ◽  
Diffusion Equations ◽  
Governing Equations ◽  
Adjoint Methods ◽  
Advection Diffusion ◽  
Runge Kutta

We develop a finite volume characteristic method for the solution of the advection-diffusion equations which model the contaminant transport through porous medium. This method uses a second order Runge-Kutta approximation for the characteristics within the framework of the Eulerian Lagrangian localized adjoint methods (ELLAM). The derived scheme conserves mass, symmetrizes the governing equations and generates accurate numerical solutions even if large time steps are used.  Numerical experiments comparing several competitive methods using a standard test example are presented to illustrate the performance of the method.  

Numerical solutions and analysis of diffusion for new generalized fractional advection-diffusion equations

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Yufeng Xu ◽  
Om Agrawal
Keyword(s):  
Finite Difference ◽  
Weight Function ◽  
Numerical Solutions ◽  
Diffusion Equations ◽  
Scale Function ◽  
Scale Functions ◽  
Advection Diffusion ◽  
The Stability ◽  
The Time Domain ◽  
Nonlinear Stretching

AbstractIn this paper we study a class of new Generalized Fractional Advection-Diffusion Equations (GFADEs) with a new Generalized Fractional Derivative (GFD) proposed last year. The new GFD is defined in the Caputo sense using a weight function and a scale function. The GFADE is discussed in a bounded domain, and numerical solutions for two examples consisting of a linear and a nonlinear GFADE are obtained using an implicit finite difference approach. The stability of the numerical scheme is investigated, and the order of convergence is estimated numerically. Numerical results illustrate that the finite difference scheme is simple and effective for solving the GFADEs. We investigate the influence of weight and scale functions on the diffusion of GFADEs. Linear and nonlinear stretching and contracting functions are considered. It is found that an increasing weight function increases the rate of diffusion, and a scale function can stretch or contract the diffusion on the time domain.

scholarly journals Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Joan Goh ◽  
Ahmad Abd. Majid ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Collocation Method ◽  
Numerical Solutions ◽  
Diffusion Equations ◽  
Test Problems ◽  
Spline Collocation ◽  
Von Neumann ◽  
One Dimensional ◽  
Advection Diffusion ◽  
The Stability ◽  
Good Agreement

Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubicB-spline. Usual finite difference scheme is used for time and space integrations. CubicB-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.

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