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