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

— 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...

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Published inBulletin of the Lebedev Physics Institute Vol. 52; no. Suppl 2; pp. S156 - S162
Main Author Kurdyumov, V. N.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.07.2025
Springer Nature B.V
Subjects
Cylindrical coordinates
Exact solutions
Finite difference method
Physics
Physics and Astronomy
Pipes
Singularities
finite difference method
circular channel
non-axisymmetric solutions
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ISSN1068-3356
1934-838X
DOI10.3103/S1068335624602553

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Summary:— 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.
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ISSN:1068-3356
1934-838X
DOI:10.3103/S1068335624602553