Stability of Difference Splitting Schemes for Convection Diffusion Equation

Gladky, A. V.

doi:10.1007/s10559-017-9919-5

Cited by 3 publications

(2 citation statements)

References 6 publications

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“…Substituting (20) into (19) and equating the coefficients of , we can get the following expressions:…”

Section: Approximate Analytical Results Of (9)-(10) and Discussionmentioning

confidence: 99%

“…For convection-diffusion equations, only few cases with special initial or boundary value conditions have analytical solutions. Therefore, most of the main concerns were the study of the qualitative properties of the solutions [5][6][7][8][9][10][11][12][13] and numerical study [14][15][16][17][18][19][20][21][22][23] for convection-diffusion equations. However, the very important approximate solution of convection-diffusion equation has not been well solved.…”

Section: Introductionmentioning

confidence: 99%

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Similarity Solution and Heat Transfer Characteristics for a Class of Nonlinear Convection‐Diffusion Equation with Initial Value Conditions

2019

Mathematical Problems in Engineering

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A class of nonlinear convection-diffusion equation is studied in this paper. The partial differential equation is converted into nonlinear ordinary differential equation by introducing a similarity transformation. The asymptotic analytical solutions are obtained by using double-parameter transformation perturbation expansion method (DPTPEM). The influences of convection functional coefficient k(z) and power law index n on the heat transport characteristics are discussed and shown graphically. The comparison with the numerical results is presented and it is found to be in excellent agreement. The method and technique used in this paper have the significance in studying other engineering problems.

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“…Substituting (20) into (19) and equating the coefficients of , we can get the following expressions:…”

Section: Approximate Analytical Results Of (9)-(10) and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Similarity Solution and Heat Transfer Characteristics for a Class of Nonlinear Convection‐Diffusion Equation with Initial Value Conditions

2019

Mathematical Problems in Engineering

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A Splitting Scheme for Diffusion and Heat Conduction Problems

Gladky

Gladka

2019

Cybern Syst Anal

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Adaptive ADI difference solution of quenching problems based on the 3D convection–reaction–diffusion equation

Zhu¹,

Ge²

2021

International Journal of Nonlinear Sciences and Numerical Simulation

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The 3D quenching problem reflecting solid-burn scene based on convection–reaction–diffusion equation is creatively concerned in this work. The spatial derivatives of original equation are discretized by Taylor series and the temporal derivatives are approximated by the Crank–Nicolson (CN) method. After the discrete schemes are arranged, an alternating direction implicit (ADI) scheme on adaptive grid is constructed to interpret quenching phenomena of the three-dimension (3D) equation with singularity source. Quenching time, quenching domain, and characteristics relative to temperature as well as variation of temperature over time are achieved via scientific experiment and analysis. Comparing with the 1D or 2D problem, it is harder for the 3D problem to produce quenching phenomena. Regardless of different convection functions, it can form quenching behaviors through experiments when only the elements which include degeneracy parameter, convection parameters, and domain sizes are configured properly. We hope all this can offer references for the 3D engineering problem. At the same time, it will offer support to research the relationship between quenching phenomena and degeneracy parameter, convection parameters, and domain sizes in the future, respectively.

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Stability of Difference Splitting Schemes for Convection Diffusion Equation

Cited by 3 publications

References 6 publications

Similarity Solution and Heat Transfer Characteristics for a Class of Nonlinear Convection‐Diffusion Equation with Initial Value Conditions

Similarity Solution and Heat Transfer Characteristics for a Class of Nonlinear Convection‐Diffusion Equation with Initial Value Conditions

A Splitting Scheme for Diffusion and Heat Conduction Problems

Adaptive ADI difference solution of quenching problems based on the 3D convection–reaction–diffusion equation

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