Figure 3 - uploaded by Fabio Lora
Content may be subject to copyright.
Test 3: Ryu & Jones 3b shock tube problem at t = 0.1. We show the numerical solution for ρ, vx and magnetic field By (points) compared with the exact solution (line).
Source publication
We present a new code designed to solve the equations of classical ideal magnetohydrodynamics (MHD) in three dimensions, submitted
to a constant gravitational field. The purpose of the code centres on the analysis of solar phenomena within the photosphere–corona
region. We present 1D and 2D standard tests to demonstrate the quality of the numerical...
Contexts in source publication
Context 1
... is a test containing magnetosonic rarefactions waves. The numerical solution shows only two strong and identical magnetosonic rarefractions. Our code was able to capture this structure and the results are shown in Fig. 3. ...
Context 2
... is greater than the magnetic pres- sure, which implies that β > 1. This excites fast and slow magnetoacoustic-gravity waves which are coupled. The ini- tial pulse splits into two propagating waves at time t = 37.5 s shown in Fig. 11 (top). At time t = 100 s, the two mag- netocoustic waves move upwards until z ≈ 1.4 Mm, in the same way as in Fig. 3 of ( Murawski et al. 2013). The waves continue moving until they reach the transition re- gion. This vertical perturbation produces the propagation of magnetoacoustic-gravity waves in a symmetric way, as shown in Fig. 11 at the xz and yz planes. In these two planes the propagation is seen in the same way. We also show the propagation ...
Similar publications
In this paper we show that the phase mixing of continuum Alfv\'{e}n waves
and/or continuum slow waves in magnetic structures of the solar atmosphere as,
e.g., coronal arcades, can create the illusion of wave propagation across the
magnetic field. This phenomenon could be erroneously interpreted as fast
magnetosonic waves. The cross-field propagatio...
Citations
... Equations 1 -5 are solved numerically using the Newtonian CAFE code (González-Avilés et al., 2015;González-Avilés and Guzmán, 2018) in a uniformly discretized domain. A summary of the numerical methods used is as follows: the right-hand side of Equations 1 -5 is discretized using the finite-volume approximation, the minmod limiter is used to reconstruct variables, and approximate numerical HLLE fluxes are implemented, the evolution uses the Method of Lines with a second-order Runge-Kutta integrator, and the divergence-free constraint of the magnetic field Equation 5 is treated using the extended generalized Lagrangemultiplier method, which is a particular extension of the divergence-cleaning method (Dedner et al., 2002). ...
We simulate the evolution of reconnection in solar flares to study the influence of magnetic-field strength and thermal conduction on the dynamics of the magnetic-reconnection and energy-conversion processes. For this, we solve the 2.5D resistive magnetohydrodynamics (MHD) equations with thermal conduction on a domain that contains the chromosphere-corona interface. The flare is triggered at a null point where a Gaussian resistivity distribution is maximum, and further evolution is tracked. The parameter space considers magnetic-field strength [B 0 ] between 22 G and 50 G, and thermal conductivity [κ] in the range from zero to 10 −11 W m −1 K −7/2. In this parameter space, we find that the magnetic field determines the reconnection rate, which can change by a 100% in the range of B 0 , whereas thermal conduction can induce a rate change of at most 10%. We also measure the evolution of magnetic, internal, and kinetic energies in a region just above the reconnection point and measure their interplay. For all simulations, magnetic energy dominates initially and relaxes on a time scale of about 20 seconds. In this interval, the magnetic energy drops by ≈ 50%, whereas the internal energy grows by ≈ 100%. During the process, part of the energy becomes kinetic, which pushes the reconnection jet upwards and is bigger for the bigger B 0 and smaller κ.
... In this work we present a code, constructed from scratch, that solves the equations of the MHD using AMR based on the methods for the solution of the equations developed for the unigrid original version of CAFE González-Avilés et al. 2015). This code is expected to join those others that are in production for Solar and Space Weather Physics. ...
The study of our Sun holds significant importance in Space Weather research, encompassing a diverse range of phenomena characterized by distinct temporal and spatial scales. To address these complexities, we developed CAFE-AMR, an implementation of an Adaptive Mesh Refinement (AMR) strategy coupled with a Magnetohydrodynamics (MHD) equation solver, aiming to tackle Solar Physics-related problems. CAFE-AMR employs standard fluid dynamics methods, including Finite Volume discretization, HLL and Roe class flux formulas, linear order reconstructors, second-order Runge-Kutta, and Corner Transport Upwind time stepping. In this paper, we present the core structure of CAFE-AMR, discuss and evaluate mesh refinement criteria strategies, and conduct various tests, including simulations of idealized Solar Wind models, relevant for Space Weather applications.
... We have developed this code based on the assumption that Euler equations can model the dynamics of luminous matter whereas the SP rules the dynamics of dark matter. The code results from merging CAFE, a code that solves Euler and Magnetohydrodynamics equations (González-Avilés et al. 2015), with our code that solves the 3D SP system (Guzmán et al. 2021), through Poisson equation, which is sourced by dark matter and fluid densities. ...
We introduce a tool that solves the Schr\"odinger-Euler-Poisson system of equations and allows the study of the interaction between ultralight bosonic dark matter, whose dynamics is described with the Schr\"odinger-Poisson system and luminous matter which, as a first approximation, is modeled with a single component compressible ideal fluid. The two matter fields are coupled through the Poisson equation, whose source is the addition of both, dark matter and gas densities. We describe the numerical methods used to solve the system of equations and present tests for each of the two components, that show the accuracy and convergence properties of the code. As simple possible applications we present some toy scenarios: i) the merger between a core of dark matter with a cloud of gas that could be the process of galaxy formation, ii) the merger of bosonic dark matter plus gas configurations emulating basic models of galaxy mergers, and iii) the post merger properties, including the dark-matter offset from gas and the correlation between oscillations of the bosonic core and those of the gas.
... Hence, it is key to use a proper numerical approach for the implementation of high-resolution simulation and controlling numerical oscillation. As a result, the Total Variation Diminishing (TVD) method is commonly adopted in hydrodynamic models, including shallow-water models [16,17], Navier-Stokes-based models [18,19], and magnetohydrodynamics models [20]. The TVD method is feasible for high-order spatial accuracy (generally the second-order accuracy in applications) and can effectively control oscillations near the discontinuities by steep gradients. ...
... In some previous literature, the slope-limiting method applied in this study can be called 'one-dimensional limiting' [51,52]. Nonetheless, the one-dimensional limiting process has been widely applied in the great mass of hydrodynamic models so far [18,20,25]. The results represented in Section 3 showed that the model with some slope limiters (including van Leer and MC limiter) can reproduce the hydrodynamics processes that are comparable to laboratory observations or DNS results. ...
To simulate the dynamical structures of stratified shear flows, the high-resolution Total Variation Diminishing (TVD) method is necessary and widely-used due to its high-order spatial accuracy, oscillation control, and ability to capture the well-defined structures of vortices. Lack of understanding the TVD slope limiters usually results in inaccurate numerical simulation on stratified shear flows in terms of shear instability and spatiotemporal variations of mixing. In this study, the performances of four typical TVD slope limiters, namely the minmod, van Leer, Monotonized Central (MC), and superbee limiters, were investigated on modelling stratified shear flows based on the open-source non-hydrostatic model, NHWAVE. The four slope limiters are all commonly-used and have the typical numerical characteristics. All the limiters were respectively applied in two classical test cases, namely, shear instability and lock-exchange problem. The simulation results showed that the effects of slope limiters were correlated with their characteristics of numerical dissipation (or anti-dissipation), which can influence notably the model predictions of the generation of shear instability, the development of interfacial structures, and the mixing process. In the test cases, MC limiter’s performance was the best, because it could simulate the well-defined structures of instability while not introducing noticeable error. Minmod has an excessively large dissipation, which introduced noticeable numerical errors that can influence the model accuracy and can even suppress or omit the generation of interfacial vortices. Superbee limiter, the most anti-dissipative one, usually over-predicted the instability and mixing effects in time and space domain, and was likely to cause computational instability in some cases. The performances of van Leer and MC were similar, but their predictions of the evolutions of interfacial structures and mixing could be significantly different. Besides, the co-effects of grid resolution and slope limiters were also investigated; it was found that the refinement of grids may not help to reproduce a higher-quality result with a specific slope limiter.
... Fluid dynamics can also apply to more complex scenarios, such as in astrophysical problems, including plasma and solar physics. In [5], J. J. González-Avilés et al. present a study about ideal MHD code to study the solar atmosphere and Jet formation in solar atmosphere due to magnetic reconnection [6]. The fluid dynamic behavior depends on the information of velocity, density, temperature, and pressure in terms of space and time. ...
In this work, an important model in fluid dynamics is analyzed by a new hybrid neurocomputing algorithm. We have considered the Falkner–Skan (FS) with the stream-wise pressure gradient transfer of mass over a dynamic wall. To analyze the boundary flow of the FS model, we have utilized the global search characteristic of a recently developed heuristic, the Sine Cosine Algorithm (SCA), and the local search characteristic of Sequential Quadratic Programming (SQP). Artificial neural network (ANN) architecture is utilized to construct a series solution of the mathematical model. We have called our technique the ANN-SCA-SQP algorithm. The dynamic of the FS system is observed by varying stream-wise pressure gradient mass transfer and dynamic wall. To validate the effectiveness of ANN-SCA-SQP algorithm, our solutions are compared with state-of-the-art reference solutions. We have repeated a hundred experiments to establish the robustness of our approach. Our experimental outcome validates the superiority of the ANN-SCA-SQP algorithm.
... T HIS paper presents a code designed to solve the system of resistive magnetohydrodynamics (MHD) equations with thermal conductivity, which is a generalized version of the CAFE code for ideal MHD presented in [1], and the resistive MHD code used in solar atmosphere applications in [2] and [3]. ...
... The way the equations are written is suitable to use a finite volume discretization and high-resolution shock-capturing methods. For this, we exploit the fact that each of the (1)-(5) admits to be written as an evolution of equation of the form (∂u m /∂t) + (∂ F mx /∂ x) + (∂ F my /∂y) + (∂ F mz /∂z) = S m , where m labels each of the evolved variables u m in the system (1)(2)(3)(4)(5). In these expressions, F mi are fluxes along each spatial direction and S m is a source for each variable u m . ...
... The system written in the form (1)(2)(3)(4)(5) and the description of the methods provided so far are already assuming that the cleaning method is the one used to keep the divergencefree constraint of the magnetic field small. The reason is that for most of the applications, we have used successfully this formulation. ...
We present a new code designed to solve the equations of classical magnetohydrodynamics in 3-D under the effects of magnetic resistivity and heat transfer. The purpose of the code centers on the analysis of solar phenomena within the photosphere–corona region and the study of the propagation of coronal mass ejections in the interplanetary medium. We present 1-D and 2-D standard tests to demonstrate the quality of the numerical results obtained with our code. As a new code test, we include a system directly related to solar physics: the formation of a jet triggered by magnetic reconnection. The program uses high-resolution shock-capturing methods, using HLLE, HLLC, and HLLD flux formulas combined with MINMOD, MC, and reconstructors. The divergence-free magnetic field constraint is controlled using the extended generalized Lagrange multipliers method and flux-constrained transport (Flux-CT) method. Concerning the accuracy of the numerical results, we present three important cases: first, for the self-similar current sheet test, the error with respect to the exact solution is 0.13%; second, about the violation of the divergence-free magnetic field constraint, we use the blast wave test and show the constraint is of order 10$^{−11}$; and third, related to the magnetic field reconnection, the code reproduces the predicted reconnection rate for the Sweet–Parker model
... The implementation is the same high-resolution shockcapturing method as used in González-Avilés et al. (2017), based on finite volume approximation. However, in the present paper we exploit the full three-dimensional capabilities of the Newtonian CAFE code (González-Avilés et al. 2015). A summary of the specific numerical methods is as follows. ...
Using simulated data-driven, 3D resistive MHD simulations of the solar atmosphere, we show that 3D magnetic reconnection may be responsible for the formation of jets with characteristics of Type II spicules. We numerically model the photosphere-corona region using the C7 equilibrium atmosphere model. The initial magnetic configuration is a 3D potential magnetic field, extrapolated up to the solar corona region from a dynamic realistic simulation of the solar photospheric magnetoconvection model that mimics the quiet-Sun. In this case, we consider a uniform and constant value of the magnetic resistivity of 12.56 $\Omega$ m. We have found that the formation of the jet depends on the Lorentz force, which helps to accelerate the plasma upward. Analyzing various properties of the jet dynamics, we found that the jet structure shows Doppler shift close to regions with high vorticity. The morphology, the upward velocity covering a range up to 130 km s$^{-1}$, and the timescale formation of the structure between 60 and 90 s, are similar to those expected for Type II spicules.
... T HIS paper presents a code designed to solve the system of resistive magnetohydrodynamics (MHD) equations with thermal conductivity, which is a generalized version of the CAFE code for ideal MHD presented in [1], and the resistive MHD code used in solar atmosphere applications in [2] and [3]. ...
... The way the equations are written is suitable to use a finite volume discretization and high-resolution shock-capturing methods. For this, we exploit the fact that each of the (1)-(5) admits to be written as an evolution of equation of the form (∂u m /∂t) + (∂ F mx /∂ x) + (∂ F my /∂y) + (∂ F mz /∂z) = S m , where m labels each of the evolved variables u m in the system (1)(2)(3)(4)(5). In these expressions, F mi are fluxes along each spatial direction and S m is a source for each variable u m . ...
... The system written in the form (1)(2)(3)(4)(5) and the description of the methods provided so far are already assuming that the cleaning method is the one used to keep the divergencefree constraint of the magnetic field small. The reason is that for most of the applications, we have used successfully this formulation. ...
We present a new code designed to solve the equations of classical magnetohydrodynamics (MHD) in three dimensions under the effects of magnetic resistivity and heat transfer. The purpose of the code centers on the analysis of solar phenomena within the photosphere-corona region and the study of the propagation of Coronal Mass Ejections (CMEs) in the interplanetary medium. We present 1D and 2D standard tests to demonstrate the quality of the numerical results obtained with our code. As a new code test, we include a system directly related to solar physics: the formation of a jet triggered by magnetic reconnection. The program uses high-resolution shock-capturing methods, using HLLE , HLLC and HLLD flux formulas combined with MINMOD, MC and WENO5 reconstructors. The divergence free magnetic field constraint is controlled using the extended generalized Lagrange Multipliers Method (EGLM) and Flux Constrained Transport (Flux-CT) method. Concerning the accuracy of the numerical results, we present three important cases: for the self-similar current sheet test, the error with respect to the exact solution is 0.13%; about the violation of the divergence free magnetic field constraint, we use the blast wave test and show the constraint is of order 10 −11 ; related to the magnetic field reconnection, the code reproduces the predicted reconnection rate for the Sweet-Parker model.
The study of our Sun holds significant importance in Space Weather research, encompassing a diverse range of phenomena characterized by distinct temporal and spatial scales. To address these complexities, we developed CAFE-AMR, an implementation of an Adaptive Mesh Refinement (AMR) strategy coupled with a Magnetohydrodynamics (MHD) equation solver, aiming to tackle Solar Physics-related problems. CAFE-AMR employs standard fluid dynamics methods, including Finite Volume discretization, HLL and Roe class flux formulas, linear order reconstructors, second-order Runge-Kutta, and Corner Transport Upwind time stepping. In this paper, we present the core structure of CAFE-AMR, discuss and evaluate mesh refinement criteria strategies, and conduct various tests, including simulations of idealized Solar Wind models, relevant for Space Weather applications.
We introduce a tool that solves the Schrödinger-Euler-Poisson system of equations and allows the study of the interaction between ultralight bosonic dark matter, whose dynamics is described with the Schrödinger-Poisson system and luminous matter which, as a first approximation, is modeled with a single component compressible ideal fluid. The two matter fields are coupled through the Poisson equation, whose source is the addition of both, dark matter and fluid densities. We describe the numerical methods used to solve the system of equations and present tests for each of the two components, that show the accuracy and convergence properties of the code. As simple possible applications we present some toy scenarios: i) the merger between a core of dark matter with a cloud of gas, ii) the merger of bosonic dark matter plus fluid configurations, and iii) the post merger properties, including the dark-matter offset from gas and the correlation between oscillations of the bosonic core and those of the gas.
