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Journal articles on the topic 'Curvilinear coordinates'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Suara, Gafar, and Timothy Oluwadare Idowu. "Optimum Techniques for the Conversion of Space Rectangular and Curvilinear Coordinates." European Journal of Engineering Research and Science 4, no. 10 (2019): 147–51. http://dx.doi.org/10.24018/ejers.2019.4.10.1588.

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Conversion between space rectangular (X, Y, Z) and curvilinear (φ, λ, h) coordinates is an important task in the field of Surveying, geodesy, positioning, navigation, mapping etc. Different techniques which include iterative methods, non-iterative techniques and closed form algebraic methods have been applied over the years to carry out the coordinate conversion. However, the results obtained using these techniques are deficient in one way or the other due to the inherent limitations such as inability to produce results for curvilinear coordinates when the values of X, Y and Z are subsequently

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2

Suara, Gafar, and Timothy Oluwadare Idowu. "Optimum Techniques for the Conversion of Space Rectangular and Curvilinear Coordinates." European Journal of Engineering and Technology Research 4, no. 10 (2019): 147–51. http://dx.doi.org/10.24018/ejeng.2019.4.10.1588.

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Conversion between space rectangular (X, Y, Z) and curvilinear (?, ?, h) coordinates is an important task in the field of Surveying, geodesy, positioning, navigation, mapping etc. Different techniques which include iterative methods, non-iterative techniques and closed form algebraic methods have been applied over the years to carry out the coordinate conversion. However, the results obtained using these techniques are deficient in one way or the other due to the inherent limitations such as inability to produce results for curvilinear coordinates when the values of X, Y and Z are subsequently

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3

Chuiko, M. M., and O. M. Korolyova. "Solution of the mixed boundary problem for the Poisson equation on two-dimensional irregular domains." Informatics 20, no. 2 (2023): 111–20. http://dx.doi.org/10.37661/1816-0301-2023-20-2-111-120.

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Objectives. A finite-difference computational algorithm is proposed for solving a mixed boundary-value problem for the Poisson equation given in two-dimensional irregular domains.Methods. To solve the problem, generalized curvilinear coordinates are used. The physical domain is mapped to the computational domain (unit square) in the space of generalized coordinates. The original problem is written in curvilinear coordinates and approximated on a uniform grid in the computational domain.The obtained results are mapped on non-uniform boundary-fitted difference grid in the physical domain.Results

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4

Kämpfer, B., and B. Lukács. "Hydrodynamics in curvilinear coordinates." Acta Physica Hungarica 61, no. 3-4 (1987): 317–41. http://dx.doi.org/10.1007/bf03158358.

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5

Paavola, J., and E. M. Salonen. "Coping with Curvilinear Coordinates." International Journal of Mechanical Engineering Education 26, no. 4 (1998): 309–17. http://dx.doi.org/10.1177/030641909802600405.

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A systematic method to generate expressions appearing in physics and engineering and valid in curvilinear orthogonal coordinates is presented. The method, which is called ‘the method of local cartesian coordinates’ achieves the same as ‘the method of moving axes’ presented in Love [1] but with a smaller effort and with more familiar mathematical tools. The main idea is: if we have an expression valid in rectangular cartesian coordinates, a corresponding expression for curvilinear orthogonal coordinates can be formed with simple steps. Some general expressions are generated, but the method can

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6

Abrikosov, A. A. "Instantons in curvilinear coordinates." Nuclear Physics B - Proceedings Supplements 86, no. 1-3 (2000): 452–55. http://dx.doi.org/10.1016/s0920-5632(00)00603-4.

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7

Hsang, Lee Ting, An Chong Shan, and Zhai Tian Yi. "Quantization in curvilinear coordinates." International Journal of Theoretical Physics 29, no. 9 (1990): 909–33. http://dx.doi.org/10.1007/bf00673681.

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8

Nesnov, Dmitriy. "Area of correct space coordination by normal conic coordinates." Geometry & Graphics 11, no. 3 (2023): 3–11. http://dx.doi.org/10.12737/2308-4898-2023-11-3-3-11.

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The field theory is widely represented in spherical and cylindrical coordinate systems, since the mathematical apparatus of these coordinate systems is well studied. Field sources with more complex structures require new approaches to their study. The purpose of this study is to determine the correct coordination of space by normal conic coordinates. This is necessary in subsequent studies, the task of which will be to simplify the expressions for the characteristics of the field by introducing a special coordination of space, which reflect the shape of the source and/or sink of the field. For

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9

Nahmad-Achar, E., and B. F. Schutz. "Pseudotensors in asymptotically curvilinear coordinates." General Relativity and Gravitation 19, no. 7 (1987): 655–63. http://dx.doi.org/10.1007/bf00766272.

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10

CIARLET, PHILIPPE G., CRISTINEL MARDARE, and MING SHEN. "SAINT VENANT COMPATIBILITY EQUATIONS IN CURVILINEAR COORDINATES." Analysis and Applications 05, no. 03 (2007): 231–51. http://dx.doi.org/10.1142/s0219530507000973.

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We first establish that the linearized strains in curvilinear coordinates associated with a given displacement field necessarily satisfy compatibility conditions that constitute the "Saint Venant equations in curvilinear coordinates". We then show that these equations are also sufficient, in the following sense: If a symmetric matrix field defined over a simply-connected open set satisfies the Saint Venant equations in curvilinear coordinates, then its coefficients are the linearized strains associated with a displacement field. In addition, our proof provides an explicit algorithm for recover

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11

Vavilov, Dmitrii E. "The partial banana mapping: a robust linear method for impact probability estimation." Monthly Notices of the Royal Astronomical Society 492, no. 3 (2019): 4546–52. http://dx.doi.org/10.1093/mnras/stz3540.

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ABSTRACT This paper presents a robust linear method for impact probability estimation of near-Earth asteroids with the Earth. This method is a significantly modified and improved method, which uses a special curvilinear coordinate system associated with the nominal orbit of an asteroid. One of the coordinates of this system is the mean anomaly in the osculating orbit of an asteroid. A normal distribution of errors of coordinates and velocities of this system is assumed. Because of the usage of the curvilinear coordinate system, the fact that the confidence region is curved and stretched mainly

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12

HILL, J. M., and Y. M. STOKES. "A NOTE ON NAVIER–STOKES EQUATIONS WITH NONORTHOGONAL COORDINATES." ANZIAM Journal 59, no. 3 (2018): 335–48. http://dx.doi.org/10.1017/s144618111700058x.

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There are many fluid flow problems involving geometries for which a nonorthogonal curvilinear coordinate system may be the most suitable. To the authors’ knowledge, the Navier–Stokes equations for an incompressible fluid formulated in terms of an arbitrary nonorthogonal curvilinear coordinate system have not been given explicitly in the literature in the simplified form obtained herein. The specific novelty in the equations derived here is the use of the general Laplacian in arbitrary nonorthogonal curvilinear coordinates and the simplification arising from a Ricci identity for Christoffel sym

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13

Budinski, Ljubomir, Julius Fabian, and Matija Stipic. "Modeling groundwater flow by lattice Boltzmann method in curvilinear coordinates." International Journal of Modern Physics C 26, no. 02 (2015): 1550013. http://dx.doi.org/10.1142/s0129183115500138.

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In order to promote the use of the lattice Boltzmann method (LBM) for the simulation of isotropic groundwater flow in a confined aquifer with arbitrary geometry, Poisson's equation was transformed into a curvilinear coordinate system. With the metric function between the physical and the computational domain established, Poisson's equation written in Cartesian coordinates was transformed in curvilinear coordinates. Following, the appropriate equilibrium function for the D2Q9 square lattice has been defined. The resulting curvilinear formulation of the LBM for groundwater flow is capable of mod

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14

Guslienko, K. Y., and E. V. Tartakovskaya. "Hopf index of the toroidal magnetic hopfions in cylindrical and spherical dots." Low Temperature Physics 51, no. 6 (2025): 695–99. https://doi.org/10.1063/10.0036746.

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Topologically non-trivial 3D magnetization textures in the restricted curvilinear geometries are considered. 3D topological charges (the Hopf indices) are calculated for a particular case of 3D topological magnetic solitons, the toroidal hopfions in cylindrical and spherical ferromagnetic dots. The calculation method is based on the theory of toroidal hopfions developed within the classical field theory for infinite media. We exploited the property of the toroidal hopfions that the Hopf index density in any curvilinear coordinate system can be expressed as a Jacobian of the transformation from

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15

Redzic, Dragan V. "The operator ∇ in orthogonal curvilinear coordinates." European Journal of Physics 22, no. 6 (2001): 595–99. http://dx.doi.org/10.1088/0143-0807/22/6/304.

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16

CIARLET, PHILIPPE G., and SORIN MARDARE. "ON KORN'S INEQUALITIES IN CURVILINEAR COORDINATES." Mathematical Models and Methods in Applied Sciences 11, no. 08 (2001): 1379–91. http://dx.doi.org/10.1142/s0218202501001379.

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We show how the inequality of Korn's type on a surface can be established as a corollary to the three-dimensional Korn inequality in curvilinear coordinates. The proof relies in particular on a careful study of the linearized Kirchhoff–Love displacement fields inside a "shell-like" body.

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17

Kane, Thomas R., and David A. Levinson. "Orthogonal Curvilinear Coordinates and Angular Velocity." Journal of Applied Mechanics 57, no. 2 (1990): 468–70. http://dx.doi.org/10.1115/1.2892013.

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18

Hamann, D. R. "Band structure in adaptive curvilinear coordinates." Physical Review B 51, no. 15 (1995): 9508–14. http://dx.doi.org/10.1103/physrevb.51.9508.

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19

Müller, Wolfgang H., and Felix A. Reich. "Simulation of Autofrettage in Curvilinear Coordinates." PAMM 14, no. 1 (2014): 437–38. http://dx.doi.org/10.1002/pamm.201410206.

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20

Toy, Michael D., and Ramachandran D. Nair. "A Potential Enstrophy and Energy Conserving Scheme for the Shallow-Water Equations Extended to Generalized Curvilinear Coordinates." Monthly Weather Review 145, no. 3 (2017): 751–72. http://dx.doi.org/10.1175/mwr-d-16-0250.1.

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An energy and potential enstrophy conserving finite-difference scheme for the shallow-water equations is derived in generalized curvilinear coordinates. This is an extension of a scheme formulated by Arakawa and Lamb for orthogonal coordinate systems. The starting point for the present scheme is the shallow-water equations cast in generalized curvilinear coordinates, and tensor analysis is used to derive the invariant conservation properties. Preliminary tests on a flat plane with doubly periodic boundary conditions are presented. The scheme is shown to possess similar order-of-convergence err

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21

Tan, Cha-Hsiang, and Michael Pecht. "A Zonal Decomposition Methodology for Detailed Temperature Field Evaluation." Journal of Electronic Packaging 112, no. 3 (1990): 260–66. http://dx.doi.org/10.1115/1.2904376.

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A zonal decomposition technique is developed for temperature field and flux determination at both aligned and nonaligned grid interface boundaries. The method facilitates heat transfer problems commonly encountered in electronics including PWBs with multiple irregular boundaries in which numerical generation of boundary-fitted coordinates is required. To demonstrate the applicability and performance of the method, a 2-D heat conduction problem in Cartesian coordinates, a 2-D heat conduction problem in curvilinear coordinates, and a 3-D heat conduction problem in curvilinear coordinates are sol

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22

Babaev, Alimzhan. "Description of Lorentz Transformations, the Doppler Effect, Hubble's Law, and Related Phenomena in Curvilinear Coordinates by Generalized Biquaternions." American Journal of Astronomy and Astrophysics 12, no. 1 (2025): 3011296. https://doi.org/10.11648/j.ajaa.20251201.12.

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This paper presents the derivation of Lorentz transformations in curvilinear coordinates utilizing generalized biquaternions. Generalized biquaternions are rotations in curvilinear coordinates, including on the <em>tx, ty</em>, and <em>tz</em> planes. These space-time rotations are precisely the Lorentz transformations in curvilinear coordinates. The orbital rotation of the source and/or receiver, which mathematically represents the Lorentz transformation in spherical coordinates, is identified as the cause of the transverse Doppler effect. The change in wave frequency, specifically

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23

Khomasuridze, N. "Effective Solution of a Class of Boundary Value Problems of Thermoelasticity in Generalized Cylindrical Coordinates." gmj 11, no. 3 (2004): 495–514. http://dx.doi.org/10.1515/gmj.2004.495.

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Abstract A class of static boundary value problems of thermoelasticity is effectively solved for bodies bounded by coordinate surfaces of generalized cylindrical coordinates ρ, α, 𝑧 (ρ, α are orthogonal curvilinear coordinates on the plane and 𝑧 is a linear coordinate). Besides in the Cartesian system of coordinates some boundary value thermoelasticity problems are separately considered for a rectangular parallelepiped. An elastic body occupying the domain Ω = {ρ 0 < ρ < ρ 1, α 0 < α < α 1, 0 < 𝑧 < 𝑧1}, is considered to be weakly transversally isotropic (the medium is weakly

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24

Liu, Ming Qin, and Y. L. Liu. "A 2D Numerical Model for Simulation of Two-Dimensional Circular Dam-Break." Applied Mechanics and Materials 130-134 (October 2011): 2993–96. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.2993.

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The purpose of this paper is to present a 2D depth-averaged model under orthogonal curvilinear coordinates for simulating two-dimensional circular dam-break flows. The proposed model uses an orthogonal curvilinear coordinate system efficiently and accurately to simulate the flow field with irregular boundaries. As for the numerical solution procedure, The SIMPLEC solution procedure has been used for the transformed governing equations in the transformed domain. Practical application of the model is illustrated by an example, which demonstrates that the mathematical model can capture hydraulic

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25

Flídr, Erik. "Derivation of entropy production in a fluid flow in a general curvilinear coordinate system." Acta Polytechnica 63, no. 2 (2023): 103–10. http://dx.doi.org/10.14311/ap.2023.63.0103.

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The paper deals with the derivation of the entropy production in the fluid flow performed in a general curvilinear coordinate system. The derivation of the entropy production is based on the thermodynamics laws as well as on the balances of mass, momentum, and energy. A brief description of the differential geometry used in general curvilinear coordinates is presented here as well to define the used notation.The application of this approach is then shown in the evaluation of the entropy production along the suction side of the blade, where the calculation was performed using available experime

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26

Paavola, J., and E. M. Salonen. "Coping with Curvilinear Coordinates in Solid Mechanics." International Journal of Mechanical Engineering Education 32, no. 1 (2004): 1–10. http://dx.doi.org/10.7227/ijmee.32.1.1.

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27

Paavola, J., and E. M. Salonen. "Coping with Curvilinear Coordinates in Fluid Mechanics." International Journal of Mechanical Engineering Education 32, no. 1 (2004): 11–17. http://dx.doi.org/10.7227/ijmee.32.1.2.

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28

Alavi, S. A. "General Noncommuting Curvilinear Coordinates and Fluid Mechanics." Chinese Physics Letters 23, no. 10 (2006): 2637–39. http://dx.doi.org/10.1088/0256-307x/23/10/004.

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29

Ziadé, Paul, and Pierre E. Sullivan. "Bi-global stability analysis in curvilinear coordinates." Physics of Fluids 31, no. 10 (2019): 105105. http://dx.doi.org/10.1063/1.5118365.

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30

Blondin, John M., and Eric A. Lufkin. "The piecewise-parabolic method in curvilinear coordinates." Astrophysical Journal Supplement Series 88 (October 1993): 589. http://dx.doi.org/10.1086/191834.

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31

Fusco, M. "FDTD algorithm in curvilinear coordinates (EM scattering)." IEEE Transactions on Antennas and Propagation 38, no. 1 (1990): 76–89. http://dx.doi.org/10.1109/8.43592.

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32

León, M. A. González, J. Mateos Guilarte, and M. de la Torre Mayado. "Factorization of supersymmetric Hamiltonians in curvilinear coordinates." Journal of Physics: Conference Series 343 (February 8, 2012): 012040. http://dx.doi.org/10.1088/1742-6596/343/1/012040.

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33

Abrikosov, A. A. "Instantons and multi-instantons in curvilinear coordinates." Nuclear Physics B 586, no. 1-2 (2000): 589–608. http://dx.doi.org/10.1016/s0550-3213(00)00450-8.

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34

Zhao, Jidong, and Dorival Pedroso. "Strain gradient theory in orthogonal curvilinear coordinates." International Journal of Solids and Structures 45, no. 11-12 (2008): 3507–20. http://dx.doi.org/10.1016/j.ijsolstr.2008.02.011.

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35

Collino, Francis, and Peter Monk. "The Perfectly Matched Layer in Curvilinear Coordinates." SIAM Journal on Scientific Computing 19, no. 6 (1998): 2061–90. http://dx.doi.org/10.1137/s1064827596301406.

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36

Hamann, D. R. "Generalized-gradient functionals in adaptive curvilinear coordinates." Physical Review B 54, no. 3 (1996): 1568–74. http://dx.doi.org/10.1103/physrevb.54.1568.

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37

Bagdonat, T., and U. Motschmann. "3D Hybrid Simulation Code Using Curvilinear Coordinates." Journal of Computational Physics 183, no. 2 (2002): 470–85. http://dx.doi.org/10.1006/jcph.2002.7203.

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38

Cardall, Christian Y. "Fluid Dynamics in Curvilinear Coordinates without Fictitious Forces." Fluids 6, no. 10 (2021): 366. http://dx.doi.org/10.3390/fluids6100366.

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The use of curvilinear coordinates is sometimes indicated by the inherent geometry of a fluid dynamics problem, but this introduces fictitious forces into the momentum equations that spoil the strict conservative form. If one is willing to work in three dimensions, these fictitious forces can be eliminated by solving for rectangular (Cartesian) momentum components on a curvilinear mesh. A thoroughly geometric approach to fluid dynamics on spacetime demonstrates this transparently, while also giving insight into a greater unity of the relativistic and nonrelativistic cases than is usually appre

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39

Villalba, Victor M. "Separation of variables for the Klein–Gordon and Dirac equations in two-dimensional space-times with a null coordinate." Canadian Journal of Physics 68, no. 11 (1990): 1243–46. http://dx.doi.org/10.1139/p90-178.

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The separation of variables for the Klein–Gordon and Dirac equations, in the presence of electromagnetic fields, for a class of curvilinear coordinate systems with a null coordinate is presented. We show that these coordinates can be associated with a system with constant acceleration. Exact solutions for the free case and for a particle in a constant electric field are obtained. Finally, the quantum distribution of scalar massless particles in the accelerated frame of reference is computed.

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40

Babaev, Alimzhan. "Description of Lorentz Transformations, the Doppler Effect, Hubble's Law, and Related Phenomena in Curvilinear Coordinates by Generalized Biquaternions." American Journal of Astronomy and Astrophysics 12, no. 1 (2025): 9–20. https://doi.org/10.11648/j.ajaa.20251201.12.

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This paper presents the derivation of Lorentz transformations in curvilinear coordinates utilizing generalized biquaternions. Generalized biquaternions are rotations in curvilinear coordinates, including on the &lt;i&gt;tx, ty&lt;/i&gt;, and &lt;i&gt;tz&lt;/i&gt; planes. These space-time rotations are precisely the Lorentz transformations in curvilinear coordinates. The orbital rotation of the source and/or receiver, which mathematically represents the Lorentz transformation in spherical coordinates, is identified as the cause of the transverse Doppler effect. T

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41

Chuiko, M. M., and O. M. Korolyova. "Numerical solution of the mixed boundary value problem for the heat equation in two-dimensional domains of complex shape." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 60, no. 3 (2024): 216–24. http://dx.doi.org/10.29235/1561-2430-2024-60-3-216-224.

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A finite-difference computational algorithm is proposed for solving a mixed boundary value problem for heat equation given in a two-dimensional domains of complex shape. To solve the problem, generalized curvilinear coordinates are used. The physical domain is mapped to the computational domain (unit square) in the space of generalized coordinates. The original problem is written in curvilinear coordinates and approximated on a uniform grid in the computational domain. The obtained results are mapped on a non-uniform boundary-fitted difference grid in the physical domain. The second-order appr

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42

Temirbekov, Nurlan, and Kerimakyn Ainur. "Mathematical and Computational Modeling of Catalytic Converter Using Navier–Stokes Equations in Curvilinear Coordinates." Mathematics 13, no. 8 (2025): 1355. https://doi.org/10.3390/math13081355.

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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 solvin

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43

Liu, Xuyan, Yingfeng Ji, and Quanqiang Liang. "Expression of strain tensor in orthogonal curvilinear coordinates." Geodesy and Geodynamics 1, no. 1 (2010): 48–56. http://dx.doi.org/10.3724/sp.j.1246.2010.00048.

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44

Pulay, P., and B. Paizs. "Newtonian molecular dynamics in general curvilinear internal coordinates." Chemical Physics Letters 353, no. 5-6 (2002): 400–406. http://dx.doi.org/10.1016/s0009-2614(02)00051-9.

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45

Wang, Pei‐Fang. "Review of Equations of Conservation in Curvilinear Coordinates." Journal of Engineering Mechanics 118, no. 11 (1992): 2265–81. http://dx.doi.org/10.1061/(asce)0733-9399(1992)118:11(2265).

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46

Gordeziani, D., G. Avalishvili, and M. Avalishvili. "Hierarchical models of elastic shells in curvilinear coordinates." Computers & Mathematics with Applications 51, no. 12 (2006): 1789–808. http://dx.doi.org/10.1016/j.camwa.2006.01.008.

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47

Sparenberg, J. A. "Note on the stream function in curvilinear coordinates." Fluid Dynamics Research 5, no. 1 (1989): 61–67. http://dx.doi.org/10.1016/0169-5983(89)90011-7.

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48

Vimala, P., and Omega P. Blessie. "Differential Transform Method in General Orthogonal Curvilinear Coordinates." Journal of Informatics and Mathematical Sciences 10, no. 1-2 (2018): 271–78. http://dx.doi.org/10.26713/jims.v10i1-2.1052.

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49

Farokhi, Hamed, and Mergen H. Ghayesh. "Modified couple stress theory in orthogonal curvilinear coordinates." Acta Mechanica 230, no. 3 (2018): 851–69. http://dx.doi.org/10.1007/s00707-018-2331-z.

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50

Abdel-Nasser, Mohamed, Antonio Moreno, and Domenec Puig. "Temporal mammogram image registration using optimized curvilinear coordinates." Computer Methods and Programs in Biomedicine 127 (April 2016): 1–14. http://dx.doi.org/10.1016/j.cmpb.2016.01.019.

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