A High Order Compact ADI Method for Solving 3D Unsteady Convection Diffusion Problems

Ge, Yongbin

doi:10.11648/j.acm.20180701.11

Cited by 11 publications

(4 citation statements)

References 27 publications

(65 reference statements)

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“…[24] has a 19-point stencil and those in Refs. [38,39] have 27-point stencils. So, the present HOC schemes make it easy to program and save storage space.…”

Section: Discussionmentioning

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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“…[24] has a 19-point stencil and those in Refs. [38,39] have 27-point stencils. So, the present HOC schemes make it easy to program and save storage space.…”

Section: Discussionmentioning

confidence: 99%

“…As we mentioned earlier, the methods in Refs. [36][37][38][39] are only suitable for solving 3D constant coefficients problems; at the same time, the method in Ref. [36] is conditionally stable.…”

Section: Discussionmentioning

confidence: 99%

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

Jian-ying

Wang

2022

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“…Численные эксперименты проводились с разделением по физическим процессам с использованием метода RHOC ADI [28]. Вычисления проводились в квадратной области 50 × 50 на сетке 2500 × 2500 с пространственным шагом 0.02 и с шагом по времени 0.005.…”

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Modeling of wave patterns at the combustion front

Yakupov¹,

Gubernov²,

Полежаев³

2021

AND

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“…The difference minimization problem has the following form. Following works [15] and [16] we perform discretization and obtain difference problems.…”

Section: Discretization Of the Problemmentioning

confidence: 99%

Approximation of the Multidimensional Optimal Control Problem for the Heat Equation (Applicable to Computational Fluid Dynamics (CFD))

Kostikov¹,

Romanenkov²

2020

Civ Eng J

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This work is devoted to finding an estimate of the convergence rate of an algorithm for numerically solving the optimal control problem for the three-dimensional heat equation. An important aspect of the work is not only the establishment of convergence of solutions of a sequence of discrete problems to the solution of the original differential problem, but the determination of the order of convergence, which plays a very important role in applications. The paper uses the discretization method of the differential problem and the method of integral estimates. The reduction of a differential multidimensional mixed problem to a difference one is based on the approximation of the desired solution and its derivatives by difference expressions, for which the error of such an approximation is known. The idea of using integral estimates is typical for such problems, but in the multidimensional case significant technical difficulties arise. To estimate errors, we used multidimensional analogues of the integration formula by parts, Friedrichs and Poincare inequalities. The technique used in this work can be applied under some additional assumptions, and for nonlinear multidimensional mixed problems of parabolic type. To find a numerical solution, the variable direction method is used for the difference problem of a parabolic type equation. The resulting algorithm is implemented using program code written in the Python 3.7 programming language.

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A High Order Compact ADI Method for Solving 3D Unsteady Convection Diffusion Problems

Cited by 11 publications

References 27 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

Modeling of wave patterns at the combustion front

Approximation of the Multidimensional Optimal Control Problem for the Heat Equation (Applicable to Computational Fluid Dynamics (CFD))

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