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 - <p style="text-align: justify;">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.</p>