Journal of Scientific Computing

, Volume 17, Issue 1–4, pp 609–618 | Cite as

ADER: Arbitrary High Order Godunov Approach

  • V. A. Titarev
  • E. F. Toro


This paper concerns the construction of non-oscillatory schemes of very high order of accuracy in space and time, to solve non-linear hyperbolic conservation laws. The schemes result from extending the ADER approach, which is related to the ENO/WENO methodology. Our schemes are conservative, one-step, explicit and fully discrete, requiring only the computation of the inter-cell fluxes to advance the solution by a full time step; the schemes have optimal stability condition. To compute the intercell flux in one space dimension we solve a generalised Riemann problem by reducing it to the solution a sequence of m conventional Riemann problems for the kth spatial derivatives of the solution, with k=0, 1,..., m−1, where m is arbitrary and is the order of the accuracy of the resulting scheme. We provide numerical examples using schemes of up to fifth order of accuracy in both time and space.

ADER essentialy non-oscillatory Godunov generalised Riemann problem 


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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • V. A. Titarev
    • 1
  • E. F. Toro
    • 1
  1. 1.Department of Computing and MathematicsManchester Metropolitan UniversityManchesterUnited Kingdom

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