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Benitez-Llambay, P., Krapp, L., Ramos, X. S., & Kratter, K. M. (2023). RAM: Rapid Advection Algorithm on Arbitrary Meshes. Astron. J., 952(2), 106.
Abstract: The study of many astrophysical flows requires computational algorithms that can capture high Mach number flows, while resolving a large dynamic range in spatial and density scales. In this paper we present a novel method, RAM: Rapid Advection Algorithm on Arbitrary Meshes. RAM is a time-explicit method to solve the advection equation in problems with large bulk velocity on arbitrary computational grids. In comparison with standard upwind algorithms, RAM enables advection with larger time steps and lower truncation errors. Our method is based on the operator splitting technique and conservative interpolation. Depending on the bulk velocity and resolution, RAM can decrease the numerical cost of hydrodynamics by more than one order of magnitude. To quantify the truncation errors and speed-up with RAM, we perform one- and two-dimensional hydrodynamics tests. We find that the order of our method is given by the order of the conservative interpolation and that the effective speed-up is in agreement with the relative increment in time step. RAM will be especially useful for numerical studies of disk-satellite interaction, characterized by high bulk orbital velocities and nontrivial geometries. Our method dramatically lowers the computational cost of simulations that simultaneously resolve the global disk and potential well inside the Hill radius of the secondary companion.
Keywords: ORBITAL ADVECTION; MAGNETOHYDRODYNAMICS CODE; SCHEME; FLOWS; MHD; SIMULATIONS; FARGO; PPM
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Comisso, L., & Asenjo, F. A. (2021). Magnetic reconnection as a mechanism for energy extraction from rotating black holes. Phys. Rev. D., 103(2), 023014.
Abstract: Spinning black holes store rotational energy that can be extracted. When a black hole is immersed in an externally supplied magnetic field, reconnection of magnetic field lines within the ergosphere can generate negative energy (relative to infinity) particles that fall into the black hole event horizon while the other accelerated particles escape stealing energy from the black hole. We show analytically that energy extraction via magnetic reconnection is possible when the black hole spin is high (dimensionless spin a similar to 1) and the plasma is strongly magnetized (plasma magnetization sigma(0) > 1/3). The parameter space region where energy extraction is allowed depends on the plasma magnetization and the orientation of the reconnecting magnetic field lines. For sigma(0) >> 1, the asymptotic negative energy at infinity per enthalpy of the decelerated plasma that is swallowed by a maximally rotating black hole is found to be epsilon(infinity)(-) similar or equal to – root sigma(0)/3. The accelerated plasma that escapes to infinity and takes away black hole energy asymptotes the energy at infinity per enthalpy epsilon(infinity)(+) similar or equal to root 3 sigma(0).. We show that the maximum power extracted from the black hole by the escaping plasma is P-extr(max) similar to 0.1M(2) root sigma(0)w(0) (here, M is the black hole mass and w(0) is the plasma enthalpy density) for the collisionless plasma regime and one order of magnitude lower for the collisional regime. Energy extraction causes a significant spindown of the black hole when a similar to 1. The maximum efficiency of the plasma energization process via magnetic reconnection in the ergosphere is found to be eta(max) similar or equal to 3/2. Since fast magnetic reconnection in the ergosphere should occur intermittently in the scenario proposed here, the associated emission within a few gravitational radii from the black hole is expected to display a bursty nature.
Keywords: BLANDFORD-ZNAJEK MECHANISM; NEAR-INFRARED FLARES; SIMULATIONS; JETS; DRIVEN
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During, G., Josserand, C., & Rica, S. (2017). Wave turbulence theory of elastic plates. Physica D, 347, 42–73.
Abstract: This article presents the complete study of the long-time evolution of random waves of a vibrating thin elastic plate in the limit of small plate deformation so that modes of oscillations interact weakly. According to the wave turbulence theory a nonlinear wave system evolves in longtime creating a slow redistribution of the spectral energy from one mode to another. We derive step by step, following the method of cumulants expansion and multiscale asymptotic perturbations, the kinetic equation for the second order cumulants as well as the second and fourth order renormalization of the dispersion relation of the waves. We characterize the non-equilibrium evolution to an equilibrium wave spectrum, which happens to be the well known Rayleigh-Jeans distribution. Moreover we show the existence of an energy cascade, often called the Kolmogorov-Zakharov spectrum, which happens to be not simply a power law, but a logarithmic correction to the Rayleigh Jeans distribution. We perform numerical simulations confirming these scenarii, namely the equilibrium relaxation for closed systems and the existence of an energy cascade wave spectrum. Both show a good agreement between theoretical predictions and numerics. We show also some other relevant features of vibrating elastic plates, such as the existence of a self-similar wave action inverse cascade which happens to blow-up in finite time. We discuss the mechanism of the wave breakdown phenomena in elastic plates as well as the limit of strong turbulence which arises as the thickness of the plate vanishes. Finally, we discuss the role of dissipation and the connection with experiments, and the generalization of the wave turbulence theory to elastic shells. (C) 2017 Elsevier B.V. All rights reserved.
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Krapp, L., Garrido-Deutelmoser, J., Benítez-Llambay, P., & Kratter, K. M. (2024). A Fast Second-order Solver for Stiff Multifluid Dust and Gas Hydrodynamics. Astrophys. J. Suppl. Ser., 271(1), 7.
Abstract: We present MDIRK: a multifluid second-order diagonally implicit Runge-Kutta method to study momentum transfer between gas and an arbitrary number (N) of dust species. The method integrates the equations of hydrodynamics with an implicit-explicit scheme and solves the stiff source term in the momentum equation with a diagonally implicit, asymptotically stable Runge-Kutta method (DIRK). In particular, DIRK admits a simple analytical solution that can be evaluated with O(N) operations, instead of standard matrix inversion, which is O(N)3 . Therefore, the analytical solution significantly reduces the computational cost of the multifluid method, making it suitable for studying the dynamics of systems with particle-size distributions. We demonstrate that the method conserves momentum to machine precision and converges to the correct equilibrium solution with constant external acceleration. To validate our numerical method we present a series of simple hydrodynamic tests, including damping of sound waves, dusty shocks, a multifluid dusty Jeans instability, and a steady-state gas-dust drift calculation. The simplicity of MDIRK lays the groundwork to build fast high-order, asymptotically stable multifluid methods.
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Rosado-Tamariz, E., Genco, F., Campos-Amezcua, A., Markou, G., & Batres, R. (2021). Enhanced dynamic simulation approach towards the efficient mining thermal energy supply with improved operational flexibility. Int. J. Energy Res., 45, 4265–4284.
Abstract: This paper presents a thermal power plant retrofitting approach focused on improvements in the operational flexibility of existing combined cycle power plants dedicated to providing thermal energy for medium and low-temperature processes in copper mining facilities. The main motivation for this research was aimed at evaluating the operational flexibility of the electrical industry through sector coupling and its effect on solving the energy sector decarbonization issues. The research evaluates the advantages of hybridization systems for supporting the electrical and mining industries to better predict operations. The proposed approach is based on a dynamic simulation scheme that finds the optimal operating parameters of the combined heat and power (CHP) system, such as location, type, and arrangement of each component of the CHP system. The power plant dynamic simulation model was validated against data available in the literature; it was also characterized by real operational data of the San Isidro II power plant installed in Chile. Several alternatives for the cogeneration plant location, as well as the splitter system design, were investigated and then compared. A cogeneration plant design with two heating modules was selected based on the comparative study performed in this work and its CHP system was evaluated for a load reduction case study. The results were compared against a reference model. The proposed CHP system exhibited improved performance: a minimum of 15% of the exhaust gases are required to supply the thermal energy demand of the electrowinning process when a full load is considered. It was also found that an average decrease of 5% of the mechanical power at each steam turbine stage noted. Finally, the proposed CHP system's average thermodynamic efficiency is found to be 19% greater than the power plant average efficiency. Consequently, an average decrease of 32 500 tons of carbon dioxide emissions per year is predicted.
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