BIT Numerical Mathematics

, Volume 56, Issue 3, pp 951–966

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


DOI: 10.1007/s10543-015-0599-0

Cite this article as:
Lundquist, T. & Nordström, J. Bit Numer Math (2016) 56: 951. doi:10.1007/s10543-015-0599-0


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.


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

Mathematics Subject Classification

65M06 65M55 

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Mathematics, Computational MathematicsLinköping UniversityLinköpingSweden

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