# Adaptive Schrittweitensteuerung zur robusten numerischen Simulation aeroelastischer Anwendungen

- An adaptive increment control for the robust numerical simulation of aeroelastic applications

Hohn, Christoph; Ballmann, Josef (Thesis advisor)

*Aachen : Publikationsserver der RWTH Aachen University (2012, 2013)*

Dissertation / PhD Thesis

Aachen, Techn. Hochsch., Diss., 2012

Abstract

In this work the concept of a new time step control is developed for an adaptive flow solver to solve (a)synchronously (pseudo)transient problems of the fluid-structure interaction numerically robust while coupling the flow solver with a structure solver algebraically (partitioned coupling). By the analytically determined APRIORI time steps it facilitates the convergence of the applied Newton method and it is emperically observable, that the numerical method generates only physically correct iteration states. The APRIORI time steps are not chosen maximum possible. Thus it seems rational to increase the local time steps gradually until some certain upper limit is exceeded, above which divergence or a physical illegitimate iteration state appears. In this case the time integration step has to be repeated a posteriori with adequately decreased time step size. This principle of trial and error is improved by the Kalman filter and other smoothing methods to estimate the limiting factor more accurately and therefore to smooth the (erratic) convergence history. Furthermore the optimal updating Newton step is iteratively determined, which reduces the number of time step repetitions and consequently the simulation time. As a special case of asynchronous time integration the synchronous integration uses the smallest APRIORI time step and increases it, as long as the convergence criterium is fulfilled and only physically admissible iteration states are generated. Otherwise the actual time integration step is repeated with adequately decreased time step size. The upper limit for this time step control is prescribed by the user in form of a physically relevant maximum time step. Within the scope of aeroelastic applications the flows around a 2D panel and 2D profiles with NLR-7301 and BAC-3-11 shapes are investigated. Stability regions are determined by numerical simulation of these aeroelastic problems varying fluid and structure relevant parameters. The correct and stable numerical simulation of fluid-structure problems requires conservative transfers of load, torsional moment and energy in space and time. The spatially conservative interpolation of loads for section by section linear or curved grid elements is derived and combined with a (fast) octree based neighborhood search. It is used for the simulation of the transonic panel problem. These interpolation methods make a transfer of discrete or linear load distributions between fluid and structure boundary mesh feasible. The partitioned fluid-structure coupling in this work consists of staggered calls of the fluid and structure solvers. Three different coupling schemes have been investigated: the loose, the extrapolation and the fixed-point iteration coupling scheme. Only the fixed-point scheme can diminish the accumulating time lag of the other two coupling schemes completely. Banachs fixed-point theorem implies the existence of an upper limit in the choice of time steps for a convergent fixedpoint iteration coupling. The surveillance of a prescribed convergence criterium forces the fixed-point scheme to converge successfully. Although the fixed-point coupling scheme is numerically the most expensive of all considered coupling schemes, it is the most accurate one and also indispensable for an exact energy transfer between fluid and structure in time. Several other improvements have been implemented in the flow solver QUADFLOW, for example the Kalman filter and some smoothing and damping methods. Also new differentiable limiters with iterative monotony correction have been introduced, which can not be described in detail here due to space restrictions.

### Identifier

- URN: urn:nbn:de:hbz:82-opus-44075
- RWTH PUBLICATIONS: RWTH-CONV-143735