292	RWTH Publication No: 47095        2009        IGPM.pdf
TITLE	Adaptive Timestep Control for Instationary Solutions of the Euler Equations
AUTHORS	Christina Steiner, Siegfried Müller, Sebastian Noelle
ABSTRACT	In this paper we continue our work on adaptive timestep control for weakly instationary problems [29, 30]. The core of the method is a space-time splitting of adjoint error representations for target functionals due to Süli [32] and Hartmann [18]. The main new ingredients are (i) the extension from scalar, 1D, conservation laws to the 2D Euler equations of gas dynamics, (ii) the derivation of boundary conditions for a new formulation of the adjoint problem and (iii) the coupling of the adaptive time-stepping with spatial adaptation. For the spatial adaptation, we use a multiscale-based strategy developed by Müller [24], and we combine this with an implicit time discretization. The combined space-time adaptive method provides an efficient choice of timesteps for implicit computations of weakly instationary flows. The timestep will be very large in regions of stationary flow, and becomes small when a perturbation enters the flow field. The efficiency of the solver is investigated by means of an unsteady inviscid 2D flow over a bump.
KEYWORDS	compressible Euler equations, weakly instationary flows, adaptive time-stepping, adjoint error analysis, multiscale analysis.
DOI	10.1137/090752821
PUBLICATION	SIAM journal on scientific computing 32(3), 1617-1651 (2010)