Year: 2012
Communications in Computational Physics, Vol. 12 (2012), Iss. 1 : pp. 284–314
Abstract
A concept of "static reconstruction" and "dynamic reconstruction" was introduced for higher-order (third-order or more) numerical methods in our previous work. Based on this concept, a class of hybrid DG/FV methods had been developed for one-dimensional conservation law using a "hybrid reconstruction" approach, and extended to two-dimensional scalar equations on triangular and Cartesian/triangular hybrid grids. In the hybrid DG/FV schemes, the lower-order derivatives of the piecewise polynomial are computed locally in a cell by the traditional DG method (called as "dynamic reconstruction"), while the higher-order derivatives are reconstructed by the "static reconstruction" of the FV method, using the known lower-order derivatives in the cell itself and in its adjacent neighboring cells. In this paper, the hybrid DG/FV schemes are extended to two-dimensional Euler equations on triangular and Cartesian/triangular hybrid grids. Some typical test cases are presented to demonstrate the performance of the hybrid DG/FV methods, including the standard vortex evolution problem with exact solution, isentropic vortex/weak shock wave interaction, subsonic flows past a circular cylinder and a three-element airfoil (30P30N), transonic flow past a NACA0012 airfoil. The accuracy study shows that the hybrid DG/FV method achieves the desired third-order accuracy, and the applications demonstrate that they can capture the flow structure accurately, and can reduce the CPU time and memory requirement greatly than the traditional DG method with the same order of accuracy.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.210111.140711a
Communications in Computational Physics, Vol. 12 (2012), Iss. 1 : pp. 284–314
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
-
A hierarchical reconstruction for DG/FV method with low dispersion: Basic formulation and applications
Zhao, Ming | Wang, Xian | Li, Xiaojian | Liu, Zhengxian | Liu, Wei | Yang, KeComputers & Fluids, Vol. 231 (2021), Iss. P.105175
https://doi.org/10.1016/j.compfluid.2021.105175 [Citations: 0] -
A Multi-Domain Hybrid DG and WENO Method for Hyperbolic Conservation Laws on Hybrid Meshes
Cheng, Jian | Liu, TiegangCommunications in Computational Physics, Vol. 16 (2014), Iss. 4 P.1116
https://doi.org/10.4208/cicp.060313.300514a [Citations: 1] -
An Implicit Algorithm for High-Order DG/FV Schemes for Compressible Flows on 2D Arbitrary Grids
Zhang, Laiping | Li, Ming | Liu, Wei | He, XinCommunications in Computational Physics, Vol. 17 (2015), Iss. 1 P.287
https://doi.org/10.4208/cicp.091113.280714a [Citations: 3] -
High order sub-cell finite volume schemes for solving hyperbolic conservation laws I: basic formulation and one-dimensional analysis
Pan, JianHua | Ren, YuXinScience China Physics, Mechanics & Astronomy, Vol. 60 (2017), Iss. 8
https://doi.org/10.1007/s11433-017-9033-9 [Citations: 6] -
High order sub-cell finite volume schemes for solving hyperbolic conservation laws II: Extension to two-dimensional systems on unstructured grids
Pan, Jianhua | Ren, Yu-xin | Sun, YutaoJournal of Computational Physics, Vol. 338 (2017), Iss. P.165
https://doi.org/10.1016/j.jcp.2017.02.052 [Citations: 9] -
A $$P_N P_M{-} CPR $$ P N P M - C P R Framework for Hyperbolic Conservation Laws
Shi, Lei | Wang, Z. J. | Zhang, L. P. | Liu, Wei | Fu, SongJournal of Scientific Computing, Vol. 61 (2014), Iss. 2 P.281
https://doi.org/10.1007/s10915-014-9829-x [Citations: 0] -
Detached Eddy Simulation of Complex Separation Flows Over a Modern Fighter Model at High Angle of Attack
Zhang, Yang | Zhang, Laiping | He, Xin | Deng, Xiaogang | Sun, HaishengCommunications in Computational Physics, Vol. 22 (2017), Iss. 5 P.1309
https://doi.org/10.4208/cicp.OA-2016-0132 [Citations: 6] -
Some recent progress of high-order methods on structured and unstructured grids in CARDC
Zhang, H.X. | Zhang, L.P. | Zhang, S.H. | Li, Q.Computers & Fluids, Vol. 154 (2017), Iss. P.371
https://doi.org/10.1016/j.compfluid.2016.10.006 [Citations: 7] -
A class of hybrid DG/FV methods for conservation laws II: Two-dimensional cases
Zhang, Laiping | Wei, Liu | Lixin, He | Xiaogang, Deng | Hanxin, ZhangJournal of Computational Physics, Vol. 231 (2012), Iss. 4 P.1104
https://doi.org/10.1016/j.jcp.2011.03.032 [Citations: 74] -
Applications of High Order Hybrid DG/FV Schemes for Two-dimensional RANS Simulations
Li, Ming | Liu, Wei | Zhang, Laiping | He, XinProcedia Engineering, Vol. 126 (2015), Iss. P.628
https://doi.org/10.1016/j.proeng.2015.11.251 [Citations: 4] -
A class of DG/FV hybrid schemes for conservation law IV: 2D viscous flows and implicit algorithm for steady cases
Zhang, Laiping | Liu, Wei | Li, Ming | He, Xin | Zhang, HanxinComputers & Fluids, Vol. 97 (2014), Iss. P.110
https://doi.org/10.1016/j.compfluid.2014.04.002 [Citations: 24]