A class of compact finite difference schemes for solving the 2D and 3D Burgers’ equations

Yang, Xiaoxia; Ge, Yongbin; Lan, Bin

doi:10.1016/j.matcom.2021.01.009

Cited by 5 publications

(13 citation statements)

References 28 publications

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“…We find that the scheme in Ref. [43] is fourth-order in 148 space, and the schemes in Ref. [42] are fourth-and sixth-order, respectively.…”

Section: Numerical Experimentsmentioning

confidence: 68%

“…We will compare the numerical results computed by the present HOC schemes with those derived by the methods in the existing literature. We note that for the methods in [42,43], we use PHOEBESolver software (http://www.phoebesolver. com/webpde/main/index) (accessed on 2 Feburary 2022) to calculate.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…We find that with the increase of time, the solution tends to a fixed value. under pictures:T = 2; left pictures: present scheme; right pictures: HOC scheme [43].…”

Section: Numerical Experimentsmentioning

confidence: 99%

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High-Order Compact Difference Method for Solving Two- and Three-Dimensional Unsteady Convection Diffusion Reaction Equations

Jian-ying

Wang

2022

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In this paper, a type of high-order compact (HOC) finite difference method is developed for solving two- and three-dimensional unsteady convection diffusion reaction (CDR) equations with variable coefficients. Firstly, an HOC difference scheme is derived to solve the two-dimensional (2D) unsteady CDR equation. Discretization in time is carried out by Taylor series expansion and correction of the truncation error remainder, while discretization in space is based on the fourth-order compact difference formulas. The scheme is second-order accuracy in time and fourth-order accuracy in space. The unconditional stability is obtained by the von Neumann analysis method. Then, this scheme is extended to solve the three-dimensional (3D) unsteady CDR equation. It needs only a five-point stencil for 2D problems and a seven-point stencil for 3D problems. Moreover, the present schemes can solve the nonlinear Burgers equation. Finally, numerical experiments are conducted to show the good performances of the new schemes.

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“…We find that the scheme in Ref. [43] is fourth-order in 148 space, and the schemes in Ref. [42] are fourth-and sixth-order, respectively.…”

Section: Numerical Experimentsmentioning

confidence: 68%

Section: Numerical Experimentsmentioning

confidence: 99%

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High-Order Compact Difference Method for Solving Two- and Three-Dimensional Unsteady Convection Diffusion Reaction Equations

Jian-ying

Wang

2022

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“…In this section, we give the results of some numerical examples. And we report 2 L -norm which is defined by 12), the initial condition 0 ( , ) u x y is taken from the exact solution [11,12]:…”

Section: Numerical Examplesmentioning

confidence: 99%

“…are the exact value and the computed value of the solution u at LGL point i .From the table 3 and the table 4, we list norm infinity and norm relative of errors about solving(12) by the ChSC method…”

mentioning

confidence: 99%

A Triangular Spectral Element Method for the 2-D Viscous Burgers Equation

Zhang

2022

J. Phys.: Conf. Ser.

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A triangular spectral element method is established for the two-dimensional viscous Burgers equation. In the spatial direction, a new type of mapping is applied. We splice the local basis functions on each triangle into a global basis function. The second-order Crank-Nicolson/ leap-frog (CNLF) method is used for discretization in the time direction. Due to the use of a quasi-interpolation operator, the nonlinear term can be handled conveniently. We give the fully discrete scheme of the method and the implementation process of the algorithm. Numerical examples verify the effectiveness of this method.

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A computational method for nonlinear Burgers’ equation using quartic-trigonometric tension B-splines

Yiğit

Hepson²,

Allahviranloo³

2022

Math Sci

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A class of compact finite difference schemes for solving the 2D and 3D Burgers’ equations

Cited by 5 publications

References 28 publications

High-Order Compact Difference Method for Solving Two- and Three-Dimensional Unsteady Convection Diffusion Reaction Equations

High-Order Compact Difference Method for Solving Two- and Three-Dimensional Unsteady Convection Diffusion Reaction Equations

A Triangular Spectral Element Method for the 2-D Viscous Burgers Equation

A computational method for nonlinear Burgers’ equation using quartic-trigonometric tension B-splines

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