A fully implicit finite-difference scheme for two-dimensional Burgers’ equations

Bahadır, A. R.

doi:10.1016/s0096-3003(02)00091-7

Cited by 130 publications

(122 citation statements)

References 7 publications

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“…For problem 1, we have taken a 20 × 20 grid with time step t = 0.0001 and Re = 100. The computed and exact values of u and v are shown in Tables I and II along with the results given in Bahadir 9 at some typical grid point (TGP). The tabulated results show that the proposed scheme produces better result than Bahadir.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…For problem 2, computations are done with parameter values Re = 50, 100, and 20 × 20 grid, with the time step t = 0.0001 at time t = 0.625 in order to compare computed results with those given by Jain and Holla 5 and Bahadir. 9 Tables V and VI show comparisons of numerical solutions obtained using the proposed scheme at t = 0.625, with the methods of Jain and Holla 5 and Bahadir. 9 From these Tables, it can be seen that numerical results obtained by using the proposed Exponential method are in good agreement with Jain and Holla 5 and Bahadir.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…The convergence is obtained in one or two iterations while in Bahadir 9 it takes two or three iterations, in other words, CPU time by the proposed implicit Expo FDM method is less than CPU time by Bahadir. 9 The accuracy and consistency of the scheme is measured in terms of error norms …”

Section: Implicit Exponential Finite-difference Scheme For Burgermentioning

confidence: 99%

“…The numerical solution of coupled Burgers' equations has been solved by many researchers. [5][6][7][8][9][10][11][12][13] Two dimensional coupled nonlinear viscous Burgers' equations are given by…”

Section: Introductionmentioning

confidence: 99%

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

2013

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In this paper, an implicit exponential finite-difference scheme (Expo FDM) has been proposed for solving two dimensional nonlinear coupled viscous Burgers’ equations (VBEs) with appropriate initial and boundary conditions. The accuracy of the method has been illustrated by taking two numerical examples. Results are compared with exact solution and those already available in the literature by finding the L1, L2, L∞ and ER errors. Excellent numerical results indicate that the proposed scheme is efficient, reliable and robust technique for the numerical solutions of Burgers’ equation.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Implicit Exponential Finite-difference Scheme For Burgermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2013

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“…For example, one may refer to the approaches based on the finite difference method ( [2,12,16,18,20,23,27]), Galerkin method ( [11,17,33]), finite element method ( [1,8,10,19,24,28]), spectral method ( [4,6,26]) and cubic spline and sinc-function methods ( [1,24,31,32] etc. Most of the mentioned numerical approaches are using various computational techniques in spatial discretizations to get more accurate approximations.…”

Section: Introductionmentioning

confidence: 99%

A New Time Stepping Method for Solving One Dimensional Burgers' Equations

Piao¹,

Kim²,

Kim³

et al. 2012

Kyungpook mathematical journal

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Abstract. In this paper, we present a simple explicit type numerical method for discretizations in time for solving one dimensional Burgers' equations. The proposed method does not need an iteration process that may be required in most implicit methods and have good convergence and efficiency in computational sense compared to other known numerical methods. For evidences, several numerical demonstrations are also provided.

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A fourth‐order finite‐difference method for solving the system of two‐dimensional Burgers' equations

Liao

2009

Numerical Methods in Fluids

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SUMMARYA fourth-order compact finite-difference method is proposed in this paper to solve the system of two-dimensional Burgers' equations. The new method is based on the two-dimensional Hopf-Cole transformation, which transforms the system of two-dimensional Burgers' equations into a linear heat equation. The linear heat equation is then solved by an implicit fourth-order compact finite-difference scheme. A compact fourth-order formula is also developed to approximate the boundary conditions of the heat equation, while the initial condition for the heat equation is approximated using Simpson's rule to maintain the overall fourth-order accuracy. Numerical experiments have been conducted to demonstrate the efficiency and high-order accuracy of this method.

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A fully implicit finite-difference scheme for two-dimensional Burgers’ equations

Cited by 130 publications

References 7 publications

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

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

A New Time Stepping Method for Solving One Dimensional Burgers' Equations

A fourth‐order finite‐difference method for solving the system of two‐dimensional Burgers' equations

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