An h-adaptive RKDG method with troubled-cell indicator for two-dimensional hyperbolic conservation laws

Authors:
Hongqiang Zhu;Jianxian Qiu
Affiliations:
School of Natural Science, Nanjing University of Posts and Telecommunications, Nanjing, People's Republic of China 210046;School of Mathematical Sciences, Xiamen University, Xiamen, People's Republic of China 361005
Venue:
Advances in Computational Mathematics
Year:
2013

Citing 16
Cited 0

Efficient implementation of essentially non-oscillatory shock-capturing schemes

Journal of Computational Physics
TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems

Journal of Computational Physics
Parallel, adaptive finite element methods for conservation laws

Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
Parallel adaptive hp-refinement techniques for conservation laws

Applied Numerical Mathematics - Special issue on adaptive mesh refinement methods for CFD applications
Adaptive local refinement with octree load balancing for the parallel solution of three-dimensional conservation laws

Journal of Parallel and Distributed Computing - Special issue on dynamic load balancing
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems

Journal of Computational Physics
Solution of Two-Dimensional Riemann Problems of Gas Dynamics by Positive Schemes

SIAM Journal on Scientific Computing
Two-dimensional Riemann solver for Euler equations of gas dynamics

Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems

Journal of Scientific Computing
Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws

SIAM Journal on Scientific Computing
Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws

Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters

SIAM Journal on Scientific Computing
A Comparison of Troubled-Cell Indicators for Runge--Kutta Discontinuous Galerkin Methods Using Weighted Essentially Nonoscillatory Limiters

SIAM Journal on Scientific Computing
Error Control for a Class of Runge-Kutta Discontinuous Galerkin Methods for Nonlinear Conservation Laws

SIAM Journal on Numerical Analysis
Adaptive Runge-Kutta discontinuous Galerkin methods using different indicators: One-dimensional case

Journal of Computational Physics
On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes

Journal of Computational Physics

Quantified Score

Hi-index	0.00

Visualization

Abstract

In Zhu and Qiu (J Comput Phys 228:6957---6976, 2009), we systematically investigated adaptive Runge-Kutta discontinuous Galerkin (RKDG) methods for hyperbolic conservation laws with different indicators, with an objective of obtaining efficient and reliable indicators to obtain better performance for adaptive computation to save computational cost. In this follow-up paper, we extend the method to solve two-dimensional problems. Although the main idea of the method for two-dimensional case is similar to that for one-dimensional case, the extension of the implementation of the method to two-dimensional case is nontrivial because of the complexity of the adaptive mesh with hanging nodes. We lay our emphasis on the implementation details including adaptive procedure, solution projection, solution reconstruction and troubled-cell indicator. Extensive numerical experiments are presented to show the effectiveness of the method.