Volume 47, Issue 3
Adaptive Runge-Kutta Discontinuous Galerkin Methods with Modified Ghost Fluid Method for Simulating the Compressible Two-Medium Flow

Jun Zhu & Jianxian Qiu

J. Math. Study, 47 (2014), pp. 250-273.

Published online: 2014-09

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  • Abstract

In this paper, we investigate using the adaptive Runge-Kutta discontinuous Galerkin (RKDG) methods with the modified ghost fluid method (MGFM) in conjunction with the adaptive RKDG methods for solving the level set function to simulate the compressible two-medium flow in one and two dimensions. A shock detection technique (KXRCF method) is adopted as an indicator to identify the troubled cell, which serves for further numerical limiting procedure which uses a modified TVB limiter to reconstruct different degrees of freedom and an adaptive mesh refinement procedure. If the computational mesh should be refined or coarsened, and the detail of the implementation algorithm is presented on how to modulate the hanging nodes and redefine the numerical solutions of the two-medium flow and the level set function on such adaptive mesh. Extensive numerical tests are provided to illustrate the proposed adaptive methods may possess the capability of enhancing the resolutions nearby the discontinuities inside of the single medium flow region and material interfacial vicinities of the two-medium flow region.

  • Keywords

RKDG method, MGFM, two-medium flow, adaptive mesh.

  • AMS Subject Headings

65M60, 65M99, 35L65

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zhujun@nuaa.edu.cn (Jun Zhu)

jxqiu@xmu.edu.cn (Jianxian Qiu)

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  • RIS
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@Article{JMS-47-250, author = {Jun and Zhu and zhujun@nuaa.edu.cn and 11434 and College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, P.R. China and Jun Zhu and Jianxian and Qiu and jxqiu@xmu.edu.cn and 11019 and School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computation, Xiamen University, Xiamen, Fujian 361005, P.R. China and Jianxian Qiu}, title = {Adaptive Runge-Kutta Discontinuous Galerkin Methods with Modified Ghost Fluid Method for Simulating the Compressible Two-Medium Flow}, journal = {Journal of Mathematical Study}, year = {2014}, volume = {47}, number = {3}, pages = {250--273}, abstract = {

In this paper, we investigate using the adaptive Runge-Kutta discontinuous Galerkin (RKDG) methods with the modified ghost fluid method (MGFM) in conjunction with the adaptive RKDG methods for solving the level set function to simulate the compressible two-medium flow in one and two dimensions. A shock detection technique (KXRCF method) is adopted as an indicator to identify the troubled cell, which serves for further numerical limiting procedure which uses a modified TVB limiter to reconstruct different degrees of freedom and an adaptive mesh refinement procedure. If the computational mesh should be refined or coarsened, and the detail of the implementation algorithm is presented on how to modulate the hanging nodes and redefine the numerical solutions of the two-medium flow and the level set function on such adaptive mesh. Extensive numerical tests are provided to illustrate the proposed adaptive methods may possess the capability of enhancing the resolutions nearby the discontinuities inside of the single medium flow region and material interfacial vicinities of the two-medium flow region.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v47n3.14.02}, url = {http://global-sci.org/intro/article_detail/jms/9957.html} }
TY - JOUR T1 - Adaptive Runge-Kutta Discontinuous Galerkin Methods with Modified Ghost Fluid Method for Simulating the Compressible Two-Medium Flow AU - Zhu , Jun AU - Qiu , Jianxian JO - Journal of Mathematical Study VL - 3 SP - 250 EP - 273 PY - 2014 DA - 2014/09 SN - 47 DO - http://doi.org/10.4208/jms.v47n3.14.02 UR - https://global-sci.org/intro/article_detail/jms/9957.html KW - RKDG method, MGFM, two-medium flow, adaptive mesh. AB -

In this paper, we investigate using the adaptive Runge-Kutta discontinuous Galerkin (RKDG) methods with the modified ghost fluid method (MGFM) in conjunction with the adaptive RKDG methods for solving the level set function to simulate the compressible two-medium flow in one and two dimensions. A shock detection technique (KXRCF method) is adopted as an indicator to identify the troubled cell, which serves for further numerical limiting procedure which uses a modified TVB limiter to reconstruct different degrees of freedom and an adaptive mesh refinement procedure. If the computational mesh should be refined or coarsened, and the detail of the implementation algorithm is presented on how to modulate the hanging nodes and redefine the numerical solutions of the two-medium flow and the level set function on such adaptive mesh. Extensive numerical tests are provided to illustrate the proposed adaptive methods may possess the capability of enhancing the resolutions nearby the discontinuities inside of the single medium flow region and material interfacial vicinities of the two-medium flow region.

Jun Zhu & Jianxian Qiu. (2019). Adaptive Runge-Kutta Discontinuous Galerkin Methods with Modified Ghost Fluid Method for Simulating the Compressible Two-Medium Flow. Journal of Mathematical Study. 47 (3). 250-273. doi:10.4208/jms.v47n3.14.02
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