ADER schemes for scalar non-linear hyperbolic conservation laws with source terms in three-space dimensions

Authors:
E. F. Toro;V. A. Titarev
Affiliations:
Laboratory of Applied Mathematics, Faculty of Engineering, University of Trento, Trento, Italy;Department of Mathematics, Faculty of Science, University of Trento, Trento, 38080 Povo, Italy
Venue:
Journal of Computational Physics
Year:
2005

Citing 13
Cited 13

Uniformly high order accurate essentially non-oscillatory schemes, 111

Journal of Computational Physics
Multidimensional upwind methods for hyperbolic conservation laws

Journal of Computational Physics
A finite-volume high-order ENO scheme for two-dimensional hyperbolic systems

Journal of Computational Physics
Weighted essentially non-oscillatory schemes

Journal of Computational Physics
Efficient implementation of weighted ENO schemes

Journal of Computational Physics
Weighted essentially non-oscillatory schemes on triangular meshes

Journal of Computational Physics
Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy

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

Journal of Scientific Computing
A technique of treating negative weights in WENO schemes

Journal of Computational Physics
ADER: A High-Order Approach for Linear Hyperbolic Systems in 2D

Journal of Scientific Computing
ADER: Arbitrary High Order Godunov Approach

Journal of Scientific Computing
Finite-volume WENO schemes for three-dimensional conservation laws

Journal of Computational Physics
TVD Fluxes for the High-Order ADER Schemes

Journal of Scientific Computing

MUSTA: a multi-stage numerical flux

Applied Numerical Mathematics - Selected papers from the first Chilean workshop on numerical analysis of partial differential equations (WONAPDE 2004)
Direct-expansion forms of ADER schemes for conservation laws and their verification

Journal of Computational Physics
Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems

Journal of Computational Physics
Development of arbitrary-order multioperators-based schemes for parallel calculations. 1: Higher-than-fifth-order approximations to convection terms

Journal of Computational Physics
ADER schemes for the shallow water equations in channel with irregular bottom elevation

Journal of Computational Physics
Solvers for the high-order Riemann problem for hyperbolic balance laws

Journal of Computational Physics
Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws

Journal of Computational Physics
Extension of WAF Type Methods to Non-Homogeneous Shallow Water Equations with Pollutant

Journal of Scientific Computing
Very-high-order weno schemes

Journal of Computational Physics
Adaptive ADER Methods Using Kernel-Based Polyharmonic Spline WENO Reconstruction

SIAM Journal on Scientific Computing
A Three-Dimensional, Unsplit Godunov Method for Scalar Conservation Laws

SIAM Journal on Scientific Computing
A sub-cell WENO reconstruction method for spatial derivatives in the ADER scheme

Journal of Computational Physics
A second order PVM flux limiter method. Application to magnetohydrodynamics and shallow stratified flows

Journal of Computational Physics

Quantified Score

Hi-index	31.49

Visualization

Abstract

In this paper we develop non-linear ADER schemes for time-dependent scalar linear and non-linear conservation laws in one-, two- and three-space dimensions. Numerical results of schemes of up to fifth order of accuracy in both time and space illustrate that the designed order of accuracy is achieved in all space dimensions for a fixed Courant number and essentially non-oscillatory results are obtained for solutions with discontinuities. We also present preliminary results for two-dimensional non-linear systems.