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Abstract— <p>A simple procedure for implementing of a finite-difference method for nonasisymmetric problems in cylindrical coordinates is explored. The treatment of axis singularity is based on an obvious physical assumption about the absence of physical singularity at the axis. The proposed method is applied to a nonaxisymmetric Graetz problem in pipes. The numerical results are compared with the analytical solution in the form of series.</p>

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Addressing Axial Singularities in the Cylindrical Laplacian for Nonaxisymmetric Simulations: An Example of the Graetz Problem in Pipes

  • 期刊论文

  • 发表日期：

    2025年7月28日

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  • V. N. Kurdyumov

摘要

Abstract—

A simple procedure for implementing of a finite-difference method for nonasisymmetric problems in cylindrical coordinates is explored. The treatment of axis singularity is based on an obvious physical assumption about the absence of physical singularity at the axis. The proposed method is applied to a nonaxisymmetric Graetz problem in pipes. The numerical results are compared with the analytical solution in the form of series.