Accuracy preserving limiter for the high-order accurate solution of the Euler equations

  • Authors:

  • Christopher Michalak;Carl Ollivier-Gooch

  • Affiliations:

  • Department of Mechanical Engineering, The University of British Columbia, 2054-6250 Applied Science Lane, Vancouver, BC, Canada V6T 1Z4;Department of Mechanical Engineering, The University of British Columbia, 2054-6250 Applied Science Lane, Vancouver, BC, Canada V6T 1Z4

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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Abstract

Higher-order finite-volume methods have been shown to be more efficient than second-order methods. However, no consensus has been reached on how to eliminate the oscillations caused by solution discontinuities. Essentially non-oscillatory (ENO) schemes provide a solution but are computationally expensive to implement and may not converge well for steady-state problems. This work studies the extension of limiters used for second-order methods to the higher-order case. Requirements for accuracy and efficient convergence are discussed. A new limiting procedure is proposed. Ringleb's flow problem is used to demonstrate that nearly nominal orders of accuracy for schemes up to fourth-order can be achieved in smooth regions using the new limiter. Results for the fourth-order accurate solution of transonic flow demonstrates good convergence properties and significant qualitative improvement of the solution relative the second-order method. The new limiter can also be successfully applied to reduce the dissipation of second-order schemes with minimal sacrifices in convergence properties relative to existing approaches.