Why Have the Observed High-frequency QPOs Not Been Produced by (MHD) Computer Simulations of Black Hole Accretion Disks?

We compare some predictions of Wagoner & Tandon (WT) with the results of the hydrodynamic and magnetohydrodynamic (MHD) simulations of Reynolds & Miller (RM). It appears that the MHD simulations were not run for long enough and the numerical damping was not small enough to produce the observed high-frequency QPOs (and the g-mode seen in the hydro simulations).

Inconsistent Global Kinetic Energy Spectra in Reanalyses and Models

Global upper tropospheric kinetic energy (KE) spectra in several global atmospheric circulation datasets are examined. The datasets considered include the ERA-Interim, JRA-55, and ERA5 reanalyses and two versions of NOAA-GFS analyses at horizontal resolutions ranging from 0.7° to 0.12°. The mesoscale portions of the spectra are found to be highly inconsistent. This is shown to be mainly due to inconsistencies in the scale-dependent numerical damping and in the large contributions to the global mesoscale KE from the KE in convective regions and near orography.The spectra also generally have a steeper mesoscale slope than the -5/3 slope of the observational Nastrom-Gage spectrum pursued at many modeling centers. The sensitivity of the slope in global models to 1) stochastically perturbing diabatic tendencies and 2) decreasing the horizontal hyper-viscosity coefficient is explored in large ensembles of 10-day forecasts made with the NCEP-GFS (0.7° grid) model. Both changes lead to larger mesoscale KE and a flatter spectral slope. The effect is stronger in the modified hyper-viscosity experiment.These results show that (a) despite assimilating vastly more observations than used in the original Nastrom-Gage studies, current high-resolution global analyses still do not converge to a single “true” global mesoscale KE spectrum, and (b) model KE spectra can be made flatter not just by increasing model resolution but also by perturbing model physics and decreasing horizontal diffusion. Such sensitivities and lack of consensus on the spectral slope also raise the possibility that the true global mesoscale spectral slope may not be a precisely -5/3 slope.

Numerical Damping Calibration Study of Particle Element Method-Based Dynamic Relaxation Approach for Modeling Longwall Top-Coal Caving

When using the explicit dynamic relaxation approach (DRA) to model the quasi-static rock breakage, fragmentation, and flow problems, especially the top-coal caving question, introducing numerical damping into the solution equation is inevitable for reducing the vibration frequency and impact speed of mesh nodes, which is significantly affect the fidelity of the computation results. Although the DRA has been widely adopted to simulate top-coal caving, the reasonable value and calibration method of numerical damping are still open issues. In this study, the calibration process of reasonable numerical damping for modeling top-coal caving is investigated by comparing with the experimental results, in which several geometry parameters of the drawing funnel are selected as the calibration indexes. The result shows that the most reasonable numerical damping value is 0.07 for the numerical modeling of interval top-coal caving in extra-thick coal seams. Finally, the correlation between the numerical damping and the physical top-coal drawing process is discussed. The numerical damping indirectly reflects the fragmentation in multi scale of coal mass and friction interaction between coal particles during the caving process, which reduces the vibration intensity of the top-coal caving system and dissipates the kinetic energy.

An Improved Time Integration Method Based on Galerkin Weak Form with Controllable Numerical Dissipation

Based on the newly proposed generalized Galerkin weak form (GGW) method, a two-step time integration method with controllable numerical dissipation is presented. In the first sub-step, the GGW method is used, and in the second sub-step, a new parameter is introduced by using the idea of a trapezoidal integral. According to the numerical analysis, it can be concluded that this method is unconditionally stable and its numerical damping is controllable with the change in introduced parameters. Compared with the GGW method, this two-step scheme avoids the fast numerical dissipation in a low-frequency range. To highlight the performance of the proposed method, some numerical problems are presented and illustrated which show that this method possesses superior accuracy, stability and efficiency compared with conventional trapezoidal rule, the Wilson method, and the Bathe method. High accuracy in a low-frequency range and controllable numerical dissipation in a high-frequency range are both the merits of the method.

Elimination of Numerical Damping in the Stability Analysis of Noncompact Thermoacoustic Systems With Linearized Euler Equations

The hybrid computational fluid dynamics/computational aeroacoustics (CFD/CAA) approach represents an effective method to assess the stability of noncompact thermoacoustic systems. This paper summarizes the state-of-the-art of this method, which is currently applied for the stability prediction of a lab-scale configuration of a perfectly premixed, swirl-stabilized gas turbine combustion chamber at the Thermodynamics institute of the Technical University of Munich. Specifically, 80 operational points, for which experimentally observed stability information is readily available, are numerically investigated concerning their susceptibility to develop thermoacoustically unstable oscillations at the first transversal eigenmode of the combustor. Three contributions are considered in this work: (1) flame driving due the deformation and displacement of the flame, (2) visco-thermal losses in the acoustic boundary layer and (3) damping due to acoustically induced vortex shedding. The analysis is based on eigenfrequency computations of the Linearized Euler Equations with the stabilized finite element method (sFEM). One main advancement presented in this study is the elimination of the nonphysical impact of artificial diffusion schemes, which is necessary to produce numerically stable solutions, but falsifies the computed stability results.

Elimination of Numerical Damping in the Stability Analysis of Non-Compact Thermoacoustic Systems With Linearized Euler Equations

The hybrid Computational Fluid Dynamics/Computational AeroAcoustics (CFD/CAA) approach represents an effective method to assess the stability of non-compact thermoacoustic systems. This paper summarizes the state-of-the-art of this method, which is currently applied for the stability prediction of a lab-scale configuration of a perfectly-premixed, swirl-stabilized gas turbine combustion chamber at the Thermodynamics institute of the Technical University of Munich. Specifically, 80 operational points, for which experimentally observed stability information is readily available, are numerically investigated concerning their susceptibility to develop thermoacoustically unstable oscillations at the first transversal eigenmode of the combustor. Three contributions are considered in this work: (1) flame driving due the deformation and displacement of the flame, (2) visco-thermal losses in the acoustic boundary layer and (3) damping due to acoustically induced vortex shedding. The analysis is based on eigenfrequency computations of the Linearized Euler Equations with the stabilized Finite Element Method (sFEM). One main advancement presented in this study is the elimination of the non-physical impact of artificial diffusion schemes, which is necessary to produce numerically stable solutions, but falsifies the computed stability results.

Vibration Response Evaluation under Shock-Type Loading with Emphasis on Finite Element Model Updating

In some cases, impulse- or shock-type excitations as the dynamic loading are inevitable, and obtaining proper response with the well-known numerical methods is not easy. This paper focuses on dynamic response estimation against short-time loading with an updated finite element model using frequency response functions (FRF) and particle swarm optimization (PSO) technique. Because there is not an analytical method for assessing the numerical responses under shock-type excitations, in this paper, experimental tests are designed on a laboratory scale to evaluate the numerical responses. The vibration responses of the system against shock loading are compared with the Newmark average acceleration scheme and also with experimental data. The results reveal that the unconditionally stable Newmark method against regular loads has an appropriate performance. Still, under short-time loading, it faces numerical damping error, and this method should not be blindly applied under shock-type loads.