Mathematical and Computational Modeling of Catalytic Converter Using Navier–Stokes Equations in Curvilinear Coordinates

Nurlan Temirbekov and Kerimakyn Ainur ()
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Nurlan Temirbekov: Faculty of Mechanics and Mathematics, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan
Kerimakyn Ainur: Faculty of Mechanics and Mathematics, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan

Mathematics, 2025, vol. 13, issue 8, 1-20

Abstract: This article discusses the problem of numerically solving the Navier–Stokes equations, the heat conduction equation, and the transport equation in the orthogonal coordinates of a free curve. Since the numerical solution domain is complex, the curvilinear mesh method was used. To do so, first, a boundary value problem was posed for the elliptic equation to automate the creation of orthogonal curved meshes. By numerically solving this problem, the program code for the curvilinear mesh generator was created. The motion of a liquid or gas through a porous medium was described by numerically solving the Navier–Stokes equations in freely curvilinear orthogonal coordinates. The transformation of the Navier–Stokes equation system, written in the stream function, vorticity variables, and cylindrical coordinates, into arbitrary curvilinear coordinates, was considered in detail by introducing metric coefficients. To solve these equations, the coefficients of which vary rapidly, a three-layer differential scheme was developed. The approximation, stability, and compactness of the differential scheme were previously studied. The considered problem was considered to be the mathematical model of a car catalytic converter, and computational experiments were conducted. Calculations were performed with the developed program code in different geometries of the computational domain and different values of grid size. The Reynolds number was changed from 100 to 10,000, and its effect on the size of the backflow in front of the porous medium was discussed. The software code, which is based on the differential equation of the Navier–Stokes equations written in the orthogonal coordinates of a curved line, and its calculation algorithm can be used for the mathematical and computer modeling of automobile catalytic converters and chemical reactors.

Keywords: Navier–Stokes equations; incompressible fluid; catalytic converter; curvilinear coordinates; finite difference scheme (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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