Efficient Fully Discrete Summation-by-Parts Schemes for Unsteady Flow Problems: An Initial Investigation

Conference paper

DOI: 10.1007/978-3-319-19800-2_31

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 106)
Cite this paper as:
Lundquist T., Nordström J. (2015) Efficient Fully Discrete Summation-by-Parts Schemes for Unsteady Flow Problems: An Initial Investigation. In: Kirby R., Berzins M., Hesthaven J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Lecture Notes in Computational Science and Engineering, vol 106. Springer, Cham

Abstract

We make an initial investigation into the temporal efficiency of a fully discrete summation-by-parts approach for stiff unsteady flows with boundary layers. 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 the results to 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.

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Mathematics, Computational MathematicsLinköping UniversityLinköpingSweden

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