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The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems
, 1997
"... This is the fifth paper in a series in which we construct and study the so-called Runge-Kutta Discontinuous Galerkin method for numerically solving hyperbolic conservation laws. In this paper, we extend the method to multidimensional nonlinear systems of conservation laws. The algorithms are describ ..."
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Cited by 508 (44 self)
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This is the fifth paper in a series in which we construct and study the so-called Runge-Kutta Discontinuous Galerkin method for numerically solving hyperbolic conservation laws. In this paper, we extend the method to multidimensional nonlinear systems of conservation laws. The algorithms
Non-Uniform Time-Step Runge-Kutta Discontinuous Galerkin Method for Computational Aeroacoustics
- Proceedings of Inter-Noise 08
, 2008
"... In computational aeroacoustics (CAA) simulations, discontinuous Galerkin space dis-cretization (DG) in conjunction with Runge-Kutta time integration (RK), which is so called Runge-Kutta discontinuous Galerkin method (RKDG), has been an attractive al-ternative to the finite difference based high-orde ..."
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Cited by 5 (1 self)
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In computational aeroacoustics (CAA) simulations, discontinuous Galerkin space dis-cretization (DG) in conjunction with Runge-Kutta time integration (RK), which is so called Runge-Kutta discontinuous Galerkin method (RKDG), has been an attractive al-ternative to the finite difference based high
Runge-Kutta discontinuous Galerkin method for
, 2012
"... We propose a high order diffuse interface method for dealing with compressible multiphase flows with interfaces. This scheme is based on the discontinuous Galerkin formulation of [1]. As it is linear, this scheme is oscillating, so that the volume fraction can become negative or greater than 1. For ..."
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We propose a high order diffuse interface method for dealing with compressible multiphase flows with interfaces. This scheme is based on the discontinuous Galerkin formulation of [1]. As it is linear, this scheme is oscillating, so that the volume fraction can become negative or greater than 1
Unified analysis of discontinuous Galerkin methods for elliptic problems
- SIAM J. Numer. Anal
, 2001
"... Abstract. We provide a framework for the analysis of a large class of discontinuous methods for second-order elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical treatment ..."
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Cited by 525 (31 self)
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Abstract. We provide a framework for the analysis of a large class of discontinuous methods for second-order elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical
Review Article Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
, 2001
"... In this paper, we review the development of the Runge–Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of ..."
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Cited by 2 (0 self)
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In this paper, we review the development of the Runge–Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety
Runge-Kutta Discontinuous Galerkin Method for Traffic Flow Model on Networks
"... Abstract. We propose a bound-preserving Runge-Kutta (RK) discontinuous Galerkin (DG) method as an efficient, effective and compact numerical approach for numerical simulation of traffic flow problems on networks, with arbitrary high order accuracy. Road networks are modeled by graphs, composed of a ..."
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Abstract. We propose a bound-preserving Runge-Kutta (RK) discontinuous Galerkin (DG) method as an efficient, effective and compact numerical approach for numerical simulation of traffic flow problems on networks, with arbitrary high order accuracy. Road networks are modeled by graphs, composed of a
A Comparison of the Performance of Limiters for Runge-Kutta Discontinuous Galerkin Methods
, 2013
"... Abstract. Discontinuities usually appear in solutions of nonlinear conservation laws even though the initial condition is smooth, which leads to great difficulty in com-puting these solutions numerically. The Runge-Kutta discontinuous Galerkin (RKDG) methods are efficientmethods for solving nonlinea ..."
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Abstract. Discontinuities usually appear in solutions of nonlinear conservation laws even though the initial condition is smooth, which leads to great difficulty in com-puting these solutions numerically. The Runge-Kutta discontinuous Galerkin (RKDG) methods are efficientmethods for solving
Runge-Kutta Central Discontinuous Galerkin BGK Method for the Navier-Stokes Equations
"... In this paper, we propose a Runge-Kutta (RK) central discontinuous Galerkin (CDG) gas-kinetic BGK method for the Navier-Stokes equations. The proposed method is based on the CDG method defined on two sets of overlapping meshes to avoid discontinuous solutions at cell interfaces, as well as the gas-k ..."
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In this paper, we propose a Runge-Kutta (RK) central discontinuous Galerkin (CDG) gas-kinetic BGK method for the Navier-Stokes equations. The proposed method is based on the CDG method defined on two sets of overlapping meshes to avoid discontinuous solutions at cell interfaces, as well as the gas
The Local Discontinuous Galerkin Method For Time-Dependent Convection-Diffusion Systems
"... In this paper, we study the Local Discontinuous Galerkin methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge-Kutta Discontinuous Galerkin methods for purely hyperbolic systems to convection-diffusion systems and share with those methods the ..."
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Cited by 300 (34 self)
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In this paper, we study the Local Discontinuous Galerkin methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge-Kutta Discontinuous Galerkin methods for purely hyperbolic systems to convection-diffusion systems and share with those methods
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