Efficient fully discrete summation-by-parts schemes for unsteady flow problems

Tomas Lundquist, Jan Nordström

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We make an initial investigation into the temporal efficiency of a fully discrete summation-by-parts approach for unsteady flows. As a model problem for the Navier–Stokes equations we consider a two-dimensional advection–diffusion problem with a boundary layer. The problem is discretized in space using finite difference approximations on summation-by-parts form together with weak boundary conditions, leading to optimal stability estimates. For the time integration part we consider various forms of high order summation-by-parts operators and compare with an existing popular fourth order diagonally implicit Runge–Kutta method. To solve the resulting fully discrete equation system, we employ a multi-grid scheme with dual time stepping.

Original languageEnglish
Pages (from-to)951-966
Number of pages16
JournalBIT Numerical Mathematics
Issue number3
Publication statusPublished - 1 Sept 2016
Externally publishedYes


  • Summation-by-parts in time
  • Temporal efficiency
  • Unsteady flow calculations

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics


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