The Runge–Kutta ray-tracing method is combined with the Monte Carlo method to analyze the radiative transfer in a three-dimensional graded-index media. The analytical solution of the trajectory of a ray in a refractive index distribution of a Maxwell fisheye lens is obtained. The temperature field, heat flux, and apparent emissivity calculated by the analytical solution of the trajectory of a ray are treated as the standard solution to verify the results of the Runge–Kutta ray-tracing methods. The third-order fixed-step, fourth-order fixed-step, and third-order variable-step Runge–Kutta ray-tracing methods are discussed here. More accurate results can be obtained by using a higher-order Runge–Kutta algorithm; however, the third-order variable-step-size Runge–Kutta ray-tracing method has better precision than the fourth-order fixed-step Runge–Kutta formula for the temperature field. The maximum relative error of the temperature as compared to the standard solution is less than 0.19%, the integrated mean relative error is less than 0.06%, and the maximum relative error of the emissivity is less than 0.94% in the case of Δ t = 10 3 . The Runge–Kutta ray-tracing method can effectively solve the radiative transfer in a three-dimensional graded-index media.


    Zugriff

    Zugriff prüfen

    Verfügbarkeit in meiner Bibliothek prüfen

    Bestellung bei Subito €


    Exportieren, teilen und zitieren



    Titel :

    Runge–Kutta Ray-Tracing Technique for Radiative Transfer in a Three-Dimensional Graded-Index Medium


    Beteiligte:
    Qian, Linfeng (Autor:in) / Shi, Guodong (Autor:in) / Huang, Yong (Autor:in)

    Erschienen in:

    Erscheinungsdatum :

    01.07.2018




    Medientyp :

    Aufsatz (Zeitschrift)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch




    Runge-Kutta Method

    Ying, Shuh-Jing (Benj | AIAA | 1997



    Explicit Runge- Kutta Integration

    L. R. Dickey | NTIS | 1966


    Multi-Step Runge- Kutta Methods

    J. S. Rosen | NTIS | 1968


    Multi-step Runge-Kutta methods

    Rosen, J. S. | NTRS | 1968