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In this article, a concept of implicit methods for scalar conservation laws in one or more spatial dimensions allowing also for source terms of various types is presented. This material is a significant extension of previous work of the first author (Breuß SIAM J. Numer. Anal. 43(3), 970–986 2005). Implicit notions are developed that are centered around a monotonicity criterion. We demonstrate a connection between a numerical scheme and a discrete entropy inequality, which is based on a classical approach by Crandall and Majda. Additionally, three implicit methods are investigated using the developed notions. Next, we conduct a convergence proof which is not based on a classical compactness argument. Finally, the theoretical results are confirmed by various numerical tests.
In current clinical cardiovascular MR (CMR) practice cardiac motion is commonly dealt with using ECG based synchronization. However, ECG is corrupted by magneto-hydrodynamic (MHD) effects in magnetic fields. This leads to artifacts in the ECG trace and evokes severe T-wave elevations, which might be misinterpreted as R-waves resulting in erroneous triggering. At (ultra)high field strengths, the propensity of ECG recordings to MHD effects is further pronounced. Pulse oximetry (POX) being inherently sensitive to blood oxygenation provides an alternative approach for cardiac gating. However, due to the travel time of the blood the peak of maximum oxygenation and hence the trigger is delayed by approx. 300 ms with respect to the ECG's R-wave. Also the peak of maximum oxygenation shows a jitter of up to 65 ms. Alternative triggering approaches include acoustic cardiac triggering (ACT). In current clinical practice cardiac gating / triggering commonly relies on using single physiological signals only. Realizing this limitation this study proposes a combined triggering approach which exploits multiple physiological signals including ECG, POX or ACT to track cardiac activity. The feasibility of the coupled approach is examined for LV function assessment at 7.0 T. For this purpose, breath-held 2D-CINE imaging in conjunction with cardiac synchronization was performed paralleled by real time logging of physiological waveforms to track (mis)synchronization between the cardiac cycle and data acquisition. Combinations of the ECG, POX and ACT signals were evaluated and processed in real time to facilitate reliable trigger information.
Improved efficiency prediction of a molten salt receiver based on dynamic cloud passage simulation
(2019)
The paper presents an aerodynamic investigation of 70 different streamlined bodies with fineness ratios ranging from 2 to 10. The bodies are chosen to idealize both unmanned and small manned aircraft fuselages and feature cross-sectional shapes that vary from circular to quadratic. The study focuses on friction and pressure drag in dependency of the individual body’s fineness ratio and cross section. The drag forces are normalized with the respective body’s wetted area to comply with an empirical drag estimation procedure. Although the friction drag coefficient then stays rather constant for all bodies, their pressure drag coefficients decrease with an increase in fineness ratio. Referring the pressure drag coefficient to the bodies’ cross-sectional areas shows a distinct pressure drag minimum at a fineness ratio of about three. The pressure drag of bodies with a quadratic cross section is generally higher than for bodies of revolution. The results are used to derive an improved form factor that can be employed in a classic empirical drag estimation method. The improved formulation takes both the fineness ratio and cross-sectional shape into account. It shows superior accuracy in estimating streamlined body drag when compared with experimental data and other form factor formulations of the literature.