The Runge{kutta Discontinuous Galerkin Method for Conservation Laws V: Multidimensional Systems

The Runge–Kutta Discontinuous Galerkin Method for Conservation Laws V

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 described and discussed, including algorithm formulation and practical implementation issues such as the...

The Runge-Kutta discontinuous Galerkin method for conservation laws V: . . .

A Runge-Kutta discontinuous Galerkin scheme for hyperbolic conservation laws with discontinuous fluxes

The paper proposes a scheme by combining the Runge-Kutta discontinuous Galerkin method with a δ-mapping algorithm for solving hyperbolic conservation laws with discontinuous fluxes. This hybrid scheme is particularly applied to nonlinear elasticity in heterogeneous media and multi-class traffic flow with inhomogeneous road conditions. Numerical examples indicate the scheme’s efficiency in resol...

A Runge-Kutta Discontinuous Galerkin Method with Conservation Constraints to Improve CFL Condition for Solving Conservation Laws

We present a new formulation of the Runge-Kutta discontinuous Galerkin (RKDG) method [7, 6, 5, 4] for conservation Laws. The new formulation requires the computed RKDG solution in a cell to satisfy additional conservation constraint in adjacent cells and does not increase the complexity or change the compactness of the RKDG method. We use this new formulation to solve conservation laws on one-d...

A Conservation Constrained Runge-Kutta Discontinuous Galerkin Method with the Improved CFL Condition for Conservation Laws

We present a new formulation of the Runge-Kutta discontinuous Galerkin (RKDG) method [6, 5, 4, 3] for conservation Laws. The new formulation requires the computed RKDG solution in a cell to satisfy additional conservation constraint in adjacent cells and does not increase the complexity or change the compactness of the RKDG method. We use this new formulation to solve conservation laws on one-d...