Numerical solutions of coupled Burgers’ equations by an implicit finite-difference scheme

Srivastava, Vineet K.; Singh, Sarita; Awasthi, Mukesh Kumar

doi:10.1063/1.4820355

Cited by 32 publications

(34 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the test problem I, we have taken a grid size 20×20 with time step ∆t = 0.0001 and Re = 100. Computed and exact values of u and v are shown in Tables II and III along with the results given by Srivastava et al 14,15 and Bahadir 9 at some typical grid point. The tabulated results show that the proposed scheme produces better results than Bahadir.…”

Section: Numerical Resultsmentioning

confidence: 96%

“…For the test problem II, numerical computations are carried out with parameters: 20×20 grid, t = 0.625, ∆t =0.0001 for Re = 50, 100 and 500, in order to compare the computed results with those given by Jain and Holla, 5 Bahadir, 9 and Srivastava et al 14,15 Table VI shows the comparisons of numerical results obtained using MCB-DQM scheme at t = 0.625 with the methods of Jain and Holla, 5 Bahadir, 9 and Srivastava et al 14,15 From Table VI, it can be noticed that the computed MCB-DQM results are in good agreement with Jain and Holla, 5 Bahadir, 9 and Srivastava et al 14,15 Fig. 3 depicts MCB-DQM computed u and v solutions corresponding to Re =50, 100 and 500 at t = 0.625.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Numerical solution of coupled Burger equation is solved by many researchers. [5][6][7][8][9][10][11][12][13][14][15] In recent years, researchers [16][17][18][19][20][21][22] proposed variant of differential quadrature method for the numerical solution of one and two dimensional linear and nonlinear differential equations. Korkmaz and Dag 23,24 proposed cubic B-spline and sinc differential quadrature methods.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical solution of two dimensional coupled viscous Burger equation using modified cubic B-spline differential quadrature method

Shukla¹,

Tamsir²,

Srivastava³

et al. 2014

AIP Advances

Self Cite

View full text Add to dashboard Cite

Quartic B-spline and two-step hybrid method applied to boundary value problem AIP Conf. Proc. 1522, 744 (2013); 10.1063/1.4801200Modified predictor-corrector multistep method using arithmetic mean for solving ordinary differential equations AIP Conf.A three-stage explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations AIP Conf.In this paper, a numerical solution of two dimensional nonlinear coupled viscous Burger equation is discussed with appropriate initial and boundary conditions using the modified cubic B-spline differential quadrature method. In this method, the weighting coefficients are computed using the modified cubic B-spline as a basis function in the differential quadrature method. Thus, the coupled Burger equation is reduced into a system of ordinary differential equations. An optimal five stage and fourth-order strong stability preserving Runge-Kutta scheme is applied for solving the resulting system of ordinary differential equations. The accuracy of the scheme is illustrated by taking two numerical examples. Computed results are compared with the exact solutions and other results available in literature. Obtained numerical result shows that the described method is efficient and reliable scheme for solving two dimensional coupled viscous Burger equation. C 2014 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx.

show abstract

Section: Numerical Resultsmentioning

confidence: 96%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical solution of two dimensional coupled viscous Burger equation using modified cubic B-spline differential quadrature method

Shukla¹,

Tamsir²,

Srivastava³

et al. 2014

AIP Advances

Self Cite

View full text Add to dashboard Cite

show abstract

“…Rashid and Ismail [21] used a Fourier pseudo-spectral method for solving the coupled Burgers' equation, and Kaya [15] has solved the coupled Burgers' equation by the Adomain decomposition method in the form of a convergent power series with easily computable components. The variational iteration method [2], the homotopy perturbation method [23], the cubic B-spline method [18] and the implicit finite-difference method [22] are used for solving the coupled Burgers' equation.…”

Section: Introductionmentioning

confidence: 99%

Haar wavelet-based numerical investigation of coupled viscous Burgers' equation

Mittal

Kaur

Mishra

2014

International Journal of Computer Mathematics

View full text Add to dashboard Cite

In this work, numerical solutions of the nonlinear coupled Burgers' equation with appropriate initial and boundary conditions in one space dimension are considered. A numerical method is proposed using the properties of uniform Haar wavelets together with a collocation method and based on semi-discretization along the space direction for solving a coupled viscous Burgers' equation. The semi-discretization scheme forms a system of nonlinear ordinary differential equations which is solved by the fourth-order RungeKutta method. Numerical experiments have been conducted in five examples to illustrate the merits of the proposed method. The relative errors L 2 and L ∞ are computed from obtained numerical results. It is shown that the proposed method is working well and produces satisfactory results.

show abstract

“…Bahadir [17] applied a finite -difference fully implicit technique to the discretization of coupled nonlinear Burger's equation and resolved the nonlinearity with the Newton's method. Other finite difference applications can be found in Srivastava et al [18], Srivastava et al [19]. These followed earlier work by Wubs and Goede [20], and Goyon [21].…”

Section: Introductionmentioning

confidence: 60%

An Element-Driven Boundary Integral Treatment for Nonlinearity: A Coupled Nonlinear Two-Dimensional Burger’s Equation Test Case

Onyejekwe¹

2017

IJFMTS

View full text Add to dashboard Cite

Abstract:To further improve on the competitiveness of the boundary element method (BEM), a hybrid version of it is used for a numerical solution of two dimensional nonlinear coupled viscous Burger's equation. Adopting this approach to a discretized 2D spatial domain, the resulting integral equations arising from the singular integral theory are applied locally to each of the elements. The resulting nonlinear discrete equations are finally solved by the Picard iteration algorithm. The simulation results obtained, not only concur with analytical solutions, but also display high accuracy and are in agreement with those available in literature.

show abstract

Numerical solutions of coupled Burgers’ equations by an implicit finite-difference scheme

Cited by 32 publications

References 12 publications

Numerical solution of two dimensional coupled viscous Burger equation using modified cubic B-spline differential quadrature method

Numerical solution of two dimensional coupled viscous Burger equation using modified cubic B-spline differential quadrature method

Haar wavelet-based numerical investigation of coupled viscous Burgers' equation

An Element-Driven Boundary Integral Treatment for Nonlinearity: A Coupled Nonlinear Two-Dimensional Burger’s Equation Test Case

Contact Info

Product

Resources

About