Stochastic goal-oriented error estimation with memory

Journal Article · Wed Nov 01 04:00:00 EDT 2017 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2017.07.009· OSTI ID:22701620

Ackmann, Jan ^[1]; Marotzke, Jochem ^[1]; Korn, Peter ^[1]

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1. Max Planck Institute for Meteorology, Bundesstraße 53, 20146 Hamburg (Germany)

We propose a stochastic dual-weighted error estimator for the viscous shallow-water equation with boundaries. For this purpose, previous work on memory-less stochastic dual-weighted error estimation is extended by incorporating memory effects. The memory is introduced by describing the local truncation error as a sum of time-correlated random variables. The random variables itself represent the temporal fluctuations in local truncation errors and are estimated from high-resolution information at near-initial times. The resulting error estimator is evaluated experimentally in two classical ocean-type experiments, the Munk gyre and the flow around an island. In these experiments, the stochastic process is adapted locally to the respective dynamical flow regime. Our stochastic dual-weighted error estimator is shown to provide meaningful error bounds for a range of physically relevant goals. We prove, as well as show numerically, that our approach can be interpreted as a linearized stochastic-physics ensemble.

• OSTI ID: 22701620
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 348; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMPUTERIZED SIMULATION
ERRORS
FLUID MECHANICS
RESOLUTION
STOCHASTIC PROCESSES