## ADER schemes for three-dimensional nonlinear hyperbolic systems (2005)

Venue: | J. Comput. Phys |

Citations: | 15 - 4 self |

### BibTeX

@ARTICLE{Titarev05aderschemes,

author = {V. A. Titarev and E. F. Toro},

title = {ADER schemes for three-dimensional nonlinear hyperbolic systems},

journal = {J. Comput. Phys},

year = {2005},

volume = {204},

pages = {204--715}

}

### OpenURL

### Abstract

In this paper we carry out the extension of the ADER approach to multidimensional non-linear systems of conservation laws. We implement non-linear schemes of up to fourth order of accuracy in both time and space. Numerical results for the compressible Euler equations illustrate the very high order of accuracy and non-oscillatory properties of the new schemes. Compared to the state-of-art finite-volume WENO schemes the ADER schemes are faster, more accurate and need less computer memory. Key words: high-order schemes, weighted essentially nonoscillatory, ADER, generalized Riemann problem, three space dimensions. 1 1