Adaptive Discontinuous Galerkin Method with Lax-Wendroff Type Time Discretization and Three-dimensional Nonconforming Tetrahedral Mesh for Euler Equations

CHINESE JOURNAL OF COMPUTATIONAL PHYSICS ›› 2013, Vol. 30 ›› Issue (6): 791-798.

Adaptive Discontinuous Galerkin Method with Lax-Wendroff Type Time Discretization and Three-dimensional Nonconforming Tetrahedral Mesh for Euler Equations

FENG Tao^1,2, YU Xijun³, AN Hengbin³, CUI Xia³, WU Di⁴, LI Zhenzhen^1,2

1. University of Science and Technology of China, Hefei 230052, China;
2. Graduate School of China Academy Engineering Physics, Beijing 100088, China;
3. National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100094, China;
4. The National University of Singapore, Singapore

Received:2012-12-21 Revised:2013-04-22 Online:2013-11-25 Published:2013-11-25

Abstract

Abstract: We present a Lax-Wendroff discontinuous Galerkin (LWDG) method combining with adaptive mesh refinement (AMR) to solve three-dimensional hyperbolic conservation laws. Compared with Runge-Kutta discontinuous finite element method (RKDG) the method has higher efficiency. We give an effective adaptive strategie. Equidistribution strategy is easily implemented on nonconforming tetrahedral mesh. Error indicator is introduced to solve three-dimensional Euler equations. Numerical experiments demonstrate that the method has satisfied numerical efficiency.

Key words: hyperbolic conservation laws, Lax-Wendroff discontinuous Galerkin method, adaptive mesh refinement

CLC Number:

O241.82

FENG Tao, YU Xijun, AN Hengbin, CUI Xia, WU Di, LI Zhenzhen. Adaptive Discontinuous Galerkin Method with Lax-Wendroff Type Time Discretization and Three-dimensional Nonconforming Tetrahedral Mesh for Euler Equations[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2013, 30(6): 791-798.

[1]	Supei ZHENG, Mangmang JIAN, Jianhu FENG, Mengqing ZHAI. Sign Preserving WENO-AO-type Central Upwind Schemes [J]. Chinese Journal of Computational Physics, 2022, 39(6): 677-686.
[2]	GUO Zitao, FENG Renzhong. A High Order Accuracy Corrected Hermite-ENO Scheme [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 36(2): 141-152.
[3]	ZHAO Fengxiang, PAN Liang, WANG Shuanghu. Weighted Essentially Non-oscillatory Schemes on Unstructured Quadrilateral Meshes [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 35(5): 525-534.
[4]	LIU Xu, XU Xiaowen, ZHANG Aiqing. A Fast Box Set Subtraction Algorithm for Parallel Structured Adaptive Mesh Refinement Applications [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 34(5): 563-573.
[5]	CHENG Xiaohan, NIE Yufeng, CAI Li, FENG Jianhu. Entropy Stable Scheme Based on Moving Meshesfor Hyperbolic Conservation Laws [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 34(2): 175-182.
[6]	GONG Xiangfei, YANG Jiming, ZHANG Shudao. A Parallel SPH Method with Background Grid of Adaptive Mesh Refinement [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 33(2): 183-189.
[7]	SUN Wenjun, FAN Zhengfeng. Adaptive Mesh Refinement Kinetic Scheme for Equations of Radiation Hydrodynamics [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 32(3): 277-292.
[8]	REN Jiong, FENG Jianhu, LIU Youqiong, LIANG Nan. High Resolution Entropy Consistent Schemes for Hyperbolic Conservation Laws [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 31(5): 539-551.
[9]	SHU Shi, YUE Xiaoqiang, ZHOU Zhiyang, XU Xiaowen. Approximation and Two-level Algorithm of Finite Volume Schemes for Diffusion Equations with Structured AMR [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 31(4): 390-402.
[10]	TANG Lingyan, SONG Songhe. An Adaptive Multiresolution Scheme for Hyperbolic Conservation Laws [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 31(2): 155-164.
[11]	XU Xiaowen, MO Zeyao, LIU Qingkai, AN Hengbin. An Implicit Time·integration Algorithm for Diffusion Equations with Structured AMR and Applications [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 29(5): 684-692.
[12]	CHEN Dawei, YU Xijun. RKCVDFEM for One-dimensional Hyperbolic Conservation Laws [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 26(4): 501-509.
[13]	XU Yun, YU Xijun. Adaptive Discontinuous Galerkin Methods for Hyperbolic Conservation Laws [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 26(2): 159-168.
[14]	LIU Guozhao, ZHANG Shudao. High Order Hybrid Centrai-WENO AMR Method for Gaseous Detonation [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2008, 25(4): 387-395.
[15]	HU Yanmei, CHEN Jianzhong, FENG Jianhu. A Fifth-order Semi-discrete Central-upwind Scheme for Hyperbolic Conservation Laws [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2008, 25(1): 29-35.

Adaptive Discontinuous Galerkin Method with Lax-Wendroff Type Time Discretization and Three-dimensional Nonconforming Tetrahedral Mesh for Euler Equations

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Authors

Reviewers

Journal Online

About Journal