Investigation and application of point implicit Runge–Kutta methods to inviscid flow problems

We derive and investigate point implicit Runge–Kutta methods to significantly improve the convergence rate to approximate steady‐state solutions of inviscid flows. It turns out that the point implicit Runge–Kutta can be interpreted as a preconditioned explicit Runge–Kutta method, where the preconditioner arises naturally as local derivative of the residual function. Moreover, many preconditioners suggested in the literature so far are identified as special case of our general ansatz. Conditions will be formulated such that explicit Runge–Kutta methods with local time stepping are equivalent to point implicit methods. In numerical examples, we will demonstrate the improved convergence rates. Copyright © 2011 John Wiley & Sons, Ltd.     

Simulation of the gelation process of hydrogel droplets in 3D bioprinting

The aim of this work is to numerically simulate the gelation of a crosslinking polymer, which is a very complex process involving chemical reactions and phase transitions from a viscous fluid to a viscoelastic solid. A phenomenological model is proposed to simulate the gelation process of agarose droplets, considering the thermal boundary conditions. The numerical model is implemented using the finite element package FlexPDE. The temperature- and time-dependent degree of gelation and the deformation of the droplets during the gelation process are investigated. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Instrumental neutron absorption activation analysis

We present and discuss a modification of instrumental neutron activation analysis (INAA) that is sensitive for nuclides that do not yield (suitable) activation products but have high cross sections for neutron absorption. Their presence in a sample may thwart INAA by neutron flux suppression inside the sample, but they remain undetected and thus unnoticed by the analyst. In particular, this refers to Li, B, Cd and Gd. The proposed method—instrumental neutron absorption activation analysis (INAAA)—takes advantage of the flux depression inside the sample caused by the neutron absorbers. It is made visible by addition of an activatable nuclide (indicator). The concentration of the neutron absorber (analyte) causes a decrease in activity of the indicator. The activity difference between a mixed sample (sample plus indicator) and the pure indicator carries the analytical information. The calibration curve hence follows a reciprocal exponential function. In a proof-of-principle experiment, the applicability for the quantification of boron was exemplified. In presence of only one neutron absorber (whose nature is known), INAAA can be applied easily for quantification of the analyte in powdered or liquid samples. Although INAAA is no trace sensitive method, it has the potential to increase the reliability of INAA analyses by fast and straightforward quality control (even in presence of two or more neutron absorbing nuclides). It is especially suited for research reactors that do not operate a prompt gamma neutron activation analysis (PGNAA) station.