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Erschienen in:
2021 | OriginalPaper | Buchkapitel
Adaptive Time Stepping Methods Within a Data Assimilation Framework Applied to Non-isothermal Flow Dynamics
verfasst von : Ferdinand Evert Uilhoorn
Erschienen in: Numerical Mathematics and Advanced Applications ENUMATH 2019
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Abstract
This contribution discusses the performance of time stepping schemes within a data assimilation framework, applied to the method of lines solutions of the non-isothermal compressible gas flow equations. We consider important classes of schemes, namely an embedded explicit Runge–Kutta (ERK) scheme, a diagonally implicit Runge–Kutta (DIRK) scheme, a fully implicit Runge–Kutta (IRK) scheme and a Rosenbrock–Krylov (ROK) scheme. For the numerical illustration, we estimated the flow transients in a subsea pipeline system. Errors from numerical discretization, missing and variability of physical parameters and inaccuracy of initial and boundary conditions are assumed non-Gaussian. Efficiency, robustness and estimation accuracy were evaluated. Results showed that the DIRK scheme is a good compromise between efficiency and robustness. Spurious oscillations were filtered out by the sequential Monte–Carlo algorithm.