Time step restrictions for Runge-Kutta discontinuous Galerkin methods on triangular grids

Authors:
Ethan J. Kubatko;Clint Dawson;Joannes J. Westerink
Affiliations:
Department of Civil and Environmental Engineering and Geodetic Science, The Ohio State University, Columbus, OH 43210, United States;Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, United States;Department of Civil Engineering and Geological Sciences, University of Notre Dame, Notre Dame, IN 46556, United States
Venue:
Journal of Computational Physics
Year:
2008

Citing 10
Cited 7

The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods

The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
An atlas of functions

An atlas of functions
Efficient implementation of essentially non-oscillatory shock-capturing schemes

Journal of Computational Physics
Total variation diminishing Runge-Kutta schemes

Mathematics of Computation
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems

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

Journal of Scientific Computing
Strong Stability-Preserving High-Order Time Discretization Methods

SIAM Review
High-order RKDG Methods for Computational Electromagnetics

Journal of Scientific Computing
Semi discrete discontinuous Galerkin methods and stage-exceeding-order, strong-stability-preserving Runge-Kutta time discretizations

Journal of Computational Physics
Dispersion and Dissipation Error in High-Order Runge-Kutta Discontinuous Galerkin Discretisations of the Maxwell Equations

Journal of Scientific Computing

Scalability of an Unstructured Grid Continuous Galerkin Based Hurricane Storm Surge Model

Journal of Scientific Computing
CFL Conditions for Runge-Kutta discontinuous Galerkin methods on triangular grids

Journal of Computational Physics
Adaptive hierarchic transformations for dynamically p-enriched slope-limiting over discontinuous Galerkin systems of generalized equations

Journal of Computational Physics
Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: Theoretical analysis and application to the Vlasov-Poisson system

Journal of Computational Physics
Short Note: A comparison of the Discontinuous-Galerkin- and Spectral-Difference-Method on triangulations using PKD polynomials

Journal of Computational Physics
Pressure forcing and dispersion analysis for discontinuous Galerkin approximations to oceanic fluid flows

Journal of Computational Physics
High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows

Journal of Computational Physics

Quantified Score

Hi-index	31.48

Visualization

Abstract

We derive CFL conditions for the linear stability of the so-called Runge-Kutta discontinuous Galerkin (RKDG) methods on triangular grids. Semidiscrete DG approximations using polynomials spaces of degree p=0,1,2, and 3 are considered and discretized in time using a number of different strong-stability-preserving (SSP) Runge-Kutta time discretization methods. Two structured triangular grid configurations are analyzed for wave propagation in different directions. Approximate relations between the two-dimensional CFL conditions derived here and previously established one-dimensional conditions can be observed after defining an appropriate triangular grid parameter h and a constant that is dependent on the polynomial degree p of the DG spatial approximation. Numerical results verify the CFL conditions that are obtained, and ''optimal'', in terms of computational efficiency, two-dimensional RKDG methods of a given order are identified.