Error Estimates for the Smagorinsky Turbulence Model: Enhanced Stability Through Scale Separation and Numerical Stabilization

In the present work we show some results on the effect of the Smagorinsky model on the stability of the associated perturbation equation. We show that in the presence of a spectral gap, such that the flow can be decomposed in a large scale with moderate gradient and a small amplitude fine scale with arbitratry gradient, the Smagorinsky model admits stability estimates for perturbations, with exponential growth depending only on the large scale gradient. We then show in the context of stabilized finite element methods that the same result carries over to the approximation and that in this context, for suitably chosen finite element spaces the Smagorinsky model acts as a stabilizer yielding close to optimal error estimates in the $$L^2$$ L 2 -norm for smooth flows in the pre-asymptotic high Reynolds number regime.

Spin-induced scalarization of Kerr black holes with a massive scalar field

In the present paper we study the onset of the spin-induced scalarization of a Kerr black hole in scalar-Gauss–Bonnet gravity with a massive scalar field. Our approach is based on a $$(2+1)$$ ( 2 + 1 ) time evolution of the relevant linearized scalar field perturbation equation. We examine the region where the Kerr black hole becomes unstable giving rise to new scalarized rotating black holes with a massive scalar field. With increasing of the scalar field mass, the minimum value of the Gauss–Bonnet coupling parameter at which scalarization is possible, increases and thus the instability region shrinks. Interestingly, the introduction of scalar field mass does not change the critical minimal value of the black hole angular momentum $$a_{\mathrm{crit}}/M$$ a crit / M where the instability of the Kerr black hole develops.

Wind noise source characterization and transmission study through a side glass of DrivAer model based on a hybrid DES/APE method

Based on a DrivAer model with notchback, the characteristics of convective and acoustic pressure fluctuations on the side window, as well as their contributions to interior noise were studied. Firstly, a full-size DrivAer clay model was produced with a real glass set on the front left window, and the rest parts with thick clay. In this way, the side glass becomes the exclusive transmission path for the exterior convective and acoustic pressures into acoustic cabin inside. In this study, the acoustic pressure fluctuation on the side window surface was calculated by solving the acoustic perturbation equation (APE) based on the calculation results of convective pressure fluctuation with the incompressible Detached Eddy Simulation (DES). Furthermore, with the convective and acoustic pressure fluctuations as power inputs, the interior noise was calculated with Statistical Energy Analysis (SEA). The calculated interior noise level shows good agreement with the tested results in the wind tunnel, which indirectly validates the reliability of the calculated acoustic pressures with APE method. The contributions of the convective and acoustic pressure fluctuations to the interior noise show that the acoustic pressure fluctuation takes much higher transmission efficiency than the convective one, especially at the high frequency range above the coincidence frequency of the glass, the contribution of acoustic pressure fluctuation is absolutely dominant.

Gravitational wave echoes induced by a point mass plunging into a black hole

Recently, the possibility of detecting gravitational wave echoes in the data stream subsequent to the binary black hole mergers observed by LIGO was suggested. Motivated by this suggestion, we presented templates of echoes based on black hole perturbations in our previous work. There, we assumed that the incident waves resulting in echoes are similar to the ones that directly escape to the asymptotic infinity. In this work, to extract more reliable information on the waveform of echoes without using the naive assumption on the incident waves, we investigate gravitational waves induced by a point mass plunging into a Kerr black hole. We solve the linear perturbation equation with the source term induced by the plunging mass under the purely outgoing boundary condition at infinity and a hypothetical reflection boundary condition near the horizon. We find that the low-frequency component below the threshold of the super-radiant instability is highly suppressed, which is consistent with the incident waveform assumed in the previous analysis. We also find that the high-frequency mode excitation is significantly larger than the one used in the previous analysis, if we adopt the perfectly reflective boundary condition independently of the frequency. When we use a simple template in which the same waveform as the direct emissions to infinity is repeated with the decreasing amplitude, the correlation between the expected signal and the template turns out to decrease very rapidly.

A self-adaptive population Rao algorithm for optimization of selected bio-energy systems

This work proposes a metaphor-less and algorithm-specific parameter-less algorithm, named as self-adaptive population Rao algorithm, for solving the single-, multi-, and many-objective optimization problems. The proposed algorithm adapts the population size based on the improvement in the fitness value during the search process. The population is randomly divided into four sub-population groups. For each sub-population, a unique perturbation equation is randomly allocated. Each perturbation equation guides the solutions toward different regions of the search space. The performance of the proposed algorithm is examined using standard optimization benchmark problems having different characteristics in the single- and multi-objective optimization scenarios. The results of the application of the proposed algorithm are compared with those obtained by the latest advanced optimization algorithms. It is observed that the results obtained by the proposed method are superior. Furthermore, the proposed algorithm is used to identify optimum design parameters through multi-objective optimization of a fertilizer-assisted microalgae cultivation process and many-objective optimization of a compression ignition biodiesel engine system. From the results of the computational tests, it is observed that the performance of the self-adaptive population Rao algorithm is superior or competitive to the other advanced optimization algorithms. The performances of the considered bio-energy systems are improved by the application of the proposed optimization algorithm. The proposed optimization algorithm is more robust and may be easily extended to solve single-, multi-, and many-objective optimization problems of different science and engineering disciplines.

Perturbation Solution for Four-Stream Infrared Radiative Transfer

A four-stream solution of the longwave radiative transfer is proposed. It is based on the exact perturbation method utilizing the absorption approximation equation as the zero-order solution. Scattering is handled by the first-order perturbation equation. The two- and four-stream approximations are compared both offline and using data from CALIPSO’s dual-wavelength lidar.

GLOBAL NEARLY-PLANE-SYMMETRIC SOLUTIONS TO THE MEMBRANE EQUATION

We prove that any simple planar travelling wave solution to the membrane equation in spatial dimension $d\geqslant 3$ with bounded spatial extent is globally nonlinearly stable under sufficiently small compactly supported perturbations, where the smallness depends on the size of the support of the perturbation as well as on the initial travelling wave profile. The main novelty of the argument is the lack of higher order peeling in our vector-field-based method. In particular, the higher order energies (in fact, all energies at order $2$ or higher) are allowed to grow polynomially (but in a controlled way) in time. This is in contrast with classical global stability arguments, where only the ‘top’ order energies used in the bootstrap argument exhibit growth, and reflects the fact that the background travelling wave solution has ‘infinite energy’ and the coefficients of the perturbation equation are not asymptotically Lorentz invariant. Nonetheless, we can prove that the perturbation converges to zero in $C^{2}$ by carefully analysing the nonlinear interactions and exposing a certain ‘vestigial’ null structure in the equations.

Instability of some k-essence spacetimes

We study the stability properties of static, spherically symmetric configurations in [Formula: see text]-essence theories with the Lagrangians of the form [Formula: see text], [Formula: see text]. The instability under spherically symmetric perturbations is proved for the two recently obtained exact solutions for [Formula: see text] and for [Formula: see text], where [Formula: see text] and [Formula: see text] are constants. The first solution describes a black hole in an asymptotically singular spacetime, the second one contains two horizons of infinite area connected by a wormhole. It is argued that spherically symmetric [Formula: see text]-essence configurations with [Formula: see text] are generically unstable because the perturbation equation is not of hyperbolic type.

Black holes in Gauss–Bonnet and Chern–Simons-scalar theory

We carry out the stability analysis of the Schwarzschild black hole in Gauss–Bonnet and Chern–Simons-scalar theory. Here, we introduce two quadratic scalar couplings ([Formula: see text]) to Gauss–Bonnet and Chern–Simons terms, where the former term is parity-even, while the latter one is parity-odd. The perturbation equation for the scalar [Formula: see text] is the Klein–Gordon equation with an effective mass, while the perturbation equation for [Formula: see text] is coupled to the parity-odd metric perturbation, providing a system of two coupled equations. It turns out that the Schwarzschild black hole is unstable against [Formula: see text] perturbation, leading to scalarized black holes, while the black hole is stable against [Formula: see text] and metric perturbations, implying no scalarized black holes.

Stability and Scalar Transport in Laminar Non-Newtonian Flow in a Bifurcating T-Junction

We consider the prototype bifurcating T-junction planar flow and compare the stability of the steady two-dimensional flow field for a Newtonian and a shear thinning inelastic fluid. Global stability of the flow to two-dimensional perturbations is analyzed using numerical solutions of the linear perturbation equation. Calculations are performed for two flow ratios between the main channel and the bifurcating channel, and for two different values of the time constant in the non-Newtonian rheological model. The results show that although the steady flow remains stable to two-dimensional perturbations for Newtonian Reynolds number up to ∼ 400, shear thinning is destabilizing in that the decay rate of the perturbation field is slower. The perturbation growth rate curves for all of the different cases may be correlated by volume averaging the local Reynolds number over the flow domain, indicating that the effect of shear thinning on stability may be described using a suitably defined average Reynolds number. These stability results provide some justification for CFD calculations of steady non-Newtonian two-dimensional flows presented in earlier papers. Since scalar transport is of interest in this flow field, we also present some numerical calculations for the Nusselt number profile along the bifurcating channel wall. The results show that for the shear thinning fluid the scalar transport rate is differentially larger by ∼ 75% across one of the bifurcating channel walls, a consequence of fluid rheology enhancing the effect of flow asymmetry in the entrance region of the bifurcation.