A Discontinuous Galerkin Scheme based on a Space-Time Expansion II. Viscous Flow Equations in Multi Dimensions

In part I of these two papers we introduced for inviscid flow in one space dimension a discontinuous Galerkin scheme of arbitrary order of accuracy in space and time. In the second part we extend the scheme to the compressible Navier-Stokes equations in multi dimensions. It is based on a space-time Taylor expansion at the old time level in which all time or mixed space-time derivatives are replaced by space derivatives using the Cauchy-Kovalevskaya procedure. The surface and volume integrals in the variational formulation are approximated by Gaussian quadrature with the values of the space-time approximate solution. The numerical fluxes at grid cell interfaces are based on the approximate solution of generalized Riemann problems for both, the inviscid and viscous part. The presented scheme has to satisfy a stability restriction similar to all other explicit DG schemes which becomes more restrictive for higher orders. The loss of efficiency, especially in the case of strongly varying sizes of grid cells is circumvented by use of different time steps in different grid cells. The presented time accurate numerical simulations run with local time steps adopted to the local stability restriction in each grid cell. In numerical simulations for the two-dimensional compressible Navier-Stokes equations we show the efficiency and the optimal order of convergence being p+1, when a polynomial approximation of degree p is used.     

Electrical simulations of doped multilayer organic light‐emitting diodes (OLEDs) under temperature stress for high current densities

Abstract— This work aims at explaining and predicting the influence of the thickness of organic materials, dye doping, and space‐charge effects on charge‐carrier transport at different operating temperatures for high current densities (50 ≤ J ≤ 7000 mA/cm²). For the purpose of determining these influences, current‐voltage characteristics for typical electrically doped multilayer organic light‐emitting diodes (OLEDs) have been simulated. The results of the simulations concur with experimental data.     

A low Mach number scheme based on multi-scale asymptotics

The low Mach number regime is characterized by a large discrepancy between the flow velocity and the speed of sound, leading to physical effects on different length scales and of different orders of magnitude. A single time scale, multiple space scale asymptotic analysis provides detailed insight into the limit behavior of solutions of the compressible Euler equations as the Mach number tends to zero. This analysis shows that “the pressure” splits up into three parts with different physical meanings. This knowledge is then used to develop a numerical scheme including multiple pressure variables to account for the different effects. The numerical method is a semi-implicit predictor-corrector algorithm. In the predictor step, the asymptotic equations are used to guess the global and large scale effects. Then the corrector step can be viewed as an incompressible solver with compressibility effects acting as source terms. Received: 28 July 1999 / Accepted: 21 September 1999     

Extension of the normal tree method

The results of this paper are applicable to linear electrical networks that may contain ideal transformers, nullors, independent and controlled sources, resistors, inductors, and capacitors, and, under a topological restriction, gyrators. A relation between summands of some expansion of the network determinant and pairs of conjugate trees is proved, which uncovers the equivalence of known criteria on generic solvability based on matroids and those based on pairs of conjugate trees. New criteria on the solvability of active networks are given. A method to obtain complete sets of generic state co‐ordinates is established, which includes the following extension of the wellknown normal tree method: The generic order of complexity equals the sum of the number of forest capacitors and the number of co–forest inductors in any normal pair of conjugate trees, the latter term being introduced in this paper. The voltages across the forest capacitors together with the currents through the co‐forest inductors may be given initial values independently from each other. Further, a systematic method of augmentation that yields networks of generic index 1 is proposed. All results are expressed in terms of network determinants as well as in terms of network graphs, and all given criteria may be checked by efficient algorithms. Copyright © 1999 John Wiley & Sons, Ltd.     

Printing with Satellite Droplets

Despite their specific methodologies, all current noncontact printing techniques such as inkjet printing (IJP), involve the break‐up of a liquid meniscus during the separation of the ink droplet from the bulk ink reservoir. Often, the break‐up of a liquid meniscus results in the formation of one or more satellite droplet whose volumes are several orders of magnitude smaller than the primary droplet. Many attempts are directed to suppress or control the formation of satellite droplets because they blur the printing result. For the first time, a simple mechanism by which a single satellite droplet is exclusively formed and directed to the substrate by a gas stream while the primary droplet remains attached to a metal rod used for controlling the formation and break‐up of the meniscus is reported. High printing resolution is demonstrated by satellite droplets printing (SDP) without the need for small orifices which are prone to clogging. Furthermore, the droplet generation from a large orifice enables SDP to handle viscous inks which has remained challenging for traditional IJP.     

Simultaneous Estradiol and Levonorgestrel Transdermal Delivery from a 7-day Patch: In Vitro and In Vivo Drug Deliveries of Three Formulations

ABSTRACT

A new drug-in-adhesive transdermal patch was developed to deliver both estradiol and levonorgestrel through the skin over a 7-day period, but at different rates. This report elucidates the in vitro and in vivo biopharmaceutical studies that were necessary during the development of this product. Three test patches had to be manufactured, all delivering estradiol at the same rate, but delivering levonorgestrel at three different rates so that a levonorgestrel dose response could be studied in the clinic. An in vitro hairless mouse skin model (HMS) using modified Franz diffusion cells was used to select the test products delivering levonorgestrel in the order of 1:2:3. HMS experiments also demonstrated that the presence of estradiol did not affect the flux of levonorgestrel. Two in vivo studies in postmenopausal women showed that at steady state (four weeks of once-weekly dosing) the three test products all delivered estradiol at comparable rates. Similarly, the levonorgestrel deliveries for the three test products were in the order expected. The target fluxes of both drugs were achieved in these three test products by varying the drug loads and patch size. That this approach was successful is evidence of the value of using the HMS penetration experiments in transdermal product development and should provide useful insights for other formulations having to develop complex systems. One of the test products is now marketed as Climara Pro^TM.     

Portable device for characterizing the angular response of UV spectroradiometers

This paper introduces a device that was developed to measure the angular response of UV spectroradiometers in the field. This device is designed to be used at the operating position of spectroradiometers; thus the derived angular response also includes any effects from imperfect leveling of the diffuser and corresponds to the actual operational angular response. The design and characterization of the device and the results from its application on 11 different spectroradiometers that operate at different European UV stations are presented. Various sources of uncertainties that were identified result in a combined uncertainty in determining the angular response, which ranges between approximately 1.5% and 10%, depending on the incidence angle and the characteristics of the diffuser. For the 11 instruments, the error in reporting the diffuse irradiance ranges between 2% and - 13%, assuming isotropic distribution of the downwelling radiances.     

Traveling reference spectroradiometer for routine quality assurance of spectral solar ultraviolet irradiance measurements

A transportable reference spectroradiometer for measuring spectral solar ultraviolet irradiance has been developed and validated. The expanded uncertainty of solar irradiance measurements with this reference spectroradiometer, based on the described methodology, is 8.8% to 4.6%, depending on the wavelength and the solar zenith angle. The accuracy of the spectroradiometer was validated by repeated site visits to two European UV monitoring sites as well as by regular comparisons with the reference spectroradiometer of the European Reference Centre for UV radiation measurements in Ispra, Italy. The spectral solar irradiance measurements of the Quality Assurance of Spectral Ultraviolet Measurements in Europe through the Development of a Transportable Unit (QASUME) spectroradiometer and these three spectroradiometers have agreed to better than 6% during the ten intercomparison campaigns held from 2002 to 2004. If the differences in irradiance scales of as much as 2% are taken into account, the agreement is of the order of 4% over the wavelength range of 300-400 nm.     

Finite-element-based computational methods for cardiovascular fluid-structure interaction

In this paper a combined arbitrary Lagrange-Euler fictitious domain (ALE-FD) method for fluid-structure interaction problems in cardiovascular biomechanics is derived in terms of a weighted residual finite-element formulation. For both fluid flow of blood and solid mechanics of vascular tissue, the performance of tetrahedral and hexahedral Crouzeix-Raviart elements are evaluated. Comparable convergence results are found, although for the test cases considered the hexahedral elements are more accurate. The possibilities that are offered by the ALE-FD method are illustrated by means of a simulation of valve dynamics in a simplified left ventricular flow model.