Compressible Magnetohydrodynamic Flows Research Articles

A staggered Lagrangian magnetohydrodynamics method based on subcell Riemann solver

This paper uses a general formalism to derive staggered Lagrangian method for 2D compressible magnetohydrodynamics (MHD) flows. A subcell method is introduced to discretize the MHD system and some Riemann problems over subcells are solved at the cell center and grid node respectively. In these solvers, only the fast-waves in all jumping relations are considered and thus the solution structure is simple. The discrete conservations of mass, momentum and energy are preserved naturally in the proposed numerical method. In order to meet the thermodynamic Gibbs relation in isentropic flows, an adaptive Riemann solver is implemented at the cell center, in which a criterion is proposed to reduce overheating errors in the rarefying problems and maintains the excellent shock-capturing ability simultaneously. It is worth to be noticed that the divergence-free condition is naturally satisfied in the Lagrangian method. Various numerical tests are presented to demonstrate the accuracy and robustness of the algorithm.

Exact and fractional solution of MHD generalized Couette hybrid nanofluid flow with Mittag–Leffler and power law kernel

This study investigates the complex behavior of Jeffrey nanofluid flow in a porous oscillating microchannel under the influence of magnetohydrodynamic (MHD) effects. The research explores how magnetic field distortions lead to diverse accumulation patterns of nanofluid particles, a phenomenon attributed to homogeneous magnetization in fluid dynamics. Nanoparticles ranging from 0.25 % to 0.5 % (low and inexpensive concentrations) are remarkably consistent for best results in most machining procedures. Different concentrations of various nanomaterial's is utilized (φ1 = φ2 = 0.01, 0.02, 0.03, 0.04) to make the simple nanfluid and hybrid nanofluid suspensions. By employing fractal-fractional derivatives governed by power law, a mathematical model developed to describe the time-varying, compressible MHD flow of Jeffrey nanofluid. The model incorporates the effects of heat transfer, pressure, and magnetic fields on the fluid dynamics. A novel fractional approach utilizing the Laplace transform is applied to solve the fractal MHD hybrid-fluid model integrated into a porous medium. The study reveals velocity flow decrease with increasing Reynolds numbers but increase with channel inclination. Additionally, both the Darcy number and magnetic field orientation enhance heat transfer rates. In addition, the velocity profile enhanced by the hybrid nanofluid suspension as compared to simple nanofluid flow. The research validates its findings by demonstrating the convergence of fractional and numerical solution methods. Furthermore, the study compares the performance of different hybrid nanofluids, concluding that water-based (H2O + GO + MoS2) hybrid fluids exhibit slightly superior characteristics compared to (CMC + GO + MoS2) hybrid nanofluids.

On steady state of viscous compressible heat conducting full magnetohydrodynamic equations

This paper is concerned with the study of equations of viscous compressible and heat-conducting full magnetohydrodynamic (MHD) steady flows in a horizontal layer under the gravitational force and a large temperature gradient across the layer. We assume as boundary conditions, periodic conditions in the horizontal directions, while in the vertical directions, slip-boundary is assumed for the velocity, vertical conditions for the magnetic field, and fixed temperature or fixed heat flux are prescribed for the temperature. The existence of stationary solution in a small neighborhood of a stationary profile close to hydrostatic state is obtained in Sobolev spaces as a fixed point of some nonlinear operator.

Strong solutions to the 3D full compressible magnetohydrodynamic flows

In this paper, we deal with the strong solutions to the full compressible magnetohydrodynamic flows in a domain Ω⊆R3. We prove the local existence and unique of strong solution under three different types of boundary conditions provided that the initial data satisfies a natural compatibility condition. The initial density of such a strong solution is allowed to contain vacuum states. Compared to the classical compressible MHD, the key issue in the limit passage is to obtain the a priori estimates of the absolute temperature, some new estimate ideas are introduced to estimate these results.

Existence and Stability of Dissipative Measure-Valued Solutions to the Full Compressible Magnetohydrodynamic Flows

Existence and Stability of Dissipative Measure-Valued Solutions to the Full Compressible Magnetohydrodynamic Flows

Global Existence and Decay Rate of Smooth Solutions for Full System of Partial Differential Equations for Three-Dimensional Compressible Magnetohydrodynamic Flows

We focus on the global existence andLp−Lqrates of convergence for the compressible magnetohydrodynamic equations inR3. We prove the global existence of smooth solutions using the standard energy method under the condition that the initial data are close to a constant equilibrium state inH3. Rates of convergence for the solution inLqnorm with2≤q≤6and its first- and second-order derivatives inL2norm are obtained, if the initial data belong toLpwith1≤p≤65.

Weak solutions to the full MHD system with non-homogeneous boundary conditions

ABSTRACT This paper is devoted to the study of weak solutions for full compressible magnetohydrodynamic flows in a 3D bounded domain, with non-homogeneous boundary condition for the velocity, absolute temperature and density on the inflow part, with Navier-type slip boundary condition for magnetic field. We show the weak–strong uniqueness principle as well as the global existence under a new notion of weak solution.

Global strong solutions of 3D compressible isothermal magnetohydrodynamics

This paper establishes the global existence of strong solutions for the three-dimensional compressible isothermal magnetohydrodynamic (MHD) flows. It is essentially shown that for the regular data with small energy but possible large oscillations, the global well-posedness of strong solutions is established.

A finite-volume scheme for modeling compressible magnetohydrodynamic flows at low Mach numbers in stellar interiors

Fully compressible magnetohydrodynamic (MHD) simulations are a fundamental tool for investigating the role of dynamo amplification in the generation of magnetic fields in deep convective layers of stars. The flows that arise in such environments are characterized by low (sonic) Mach numbers (ℳson ≲ 10−2). In these regimes, conventional MHD codes typically show excessive dissipation and tend to be inefficient as the Courant–Friedrichs–Lewy (CFL) constraint on the time step becomes too strict. In this work we present a new method for efficiently simulating MHD flows at low Mach numbers in a space-dependent gravitational potential while still retaining all effects of compressibility. The proposed scheme is implemented in the finite-volume SEVEN-LEAGUE HYDRO (SLH) code, and it makes use of a low-Mach version of the five-wave Harten–Lax–van Leer discontinuities (HLLD) solver to reduce numerical dissipation, an implicit–explicit time discretization technique based on Strang splitting to overcome the overly strict CFL constraint, and a well-balancing method that dramatically reduces the magnitude of spatial discretization errors in strongly stratified setups. The solenoidal constraint on the magnetic field is enforced by using a constrained transport method on a staggered grid. We carry out five verification tests, including the simulation of a small-scale dynamo in a star-like environment at ℳson ~ 10−3. We demonstrate that the proposed scheme can be used to accurately simulate compressible MHD flows in regimes of low Mach numbers and strongly stratified setups even with moderately coarse grids.

A robust and efficient solver based on kinetic schemes for Magnetohydrodynamics (MHD) equations

This paper is devoted to the simulation of compressible magnetohydrodynamic (MHD) flows with the Lattice Boltzmann Method (LBM). The usual LBM is limited to low-Mach flows. We propose a robust and accurate numerical method based on the vectorial kinetic construction of [5,25], which allows us to extend the LBM to arbitrary Mach flows. We also explain how to adjust the numerical viscosity in order to obtain stable and accurate results in smooth or discontinuous parts of the flow and reduced divergence errors. The method can handle shock waves and can be made second order in smooth regions. It is also very well adapted to computing with Graphics Processing Unit (GPU). Our GPU implementation in 2D achieves state-of-the-art accuracy, with near-optimal performance. We finally present numerical computations of a tilt instability that demonstrate the capability of the method to handle physically relevant simulations.

On global solutions to the 3D viscous, compressible, and heat-conducting magnetohydrodynamic flows

On global solutions to the 3D viscous, compressible, and heat-conducting magnetohydrodynamic flows

The sharp time-decay rates for one-dimensional compressible isentropic Navier-Stokes and magnetohydrodynamic flows

The sharp time-decay rates for one-dimensional compressible isentropic Navier-Stokes and magnetohydrodynamic flows

Mean fields and fluctuations in compressible magnetohydrodynamic flows

We apply Gaussian smoothing to obtain mean magnetic field, density, velocity, and magnetic and kinetic energy densities from our numerical model of the interstellar medium, based on three-dimensional magnetohydrodynamic equations in a shearing box in size. The interstellar medium is highly compressible, as the turbulence is transonic or supersonic; it is thus an excellent context in which to explore the use of smoothing to represent physical variables in a compressible medium in terms of their mean and fluctuating parts. Unlike alternative averaging procedures, such as horizontal averaging, Gaussian smoothing retains the three-dimensional structure of the mean fields. Although Gaussian smoothing does not obey the Reynolds rules of averaging, physically meaningful and mathematically sound central statistical moments are defined as suggested by Germano [Turbulence – The filtering approach. J. Fluid Mech. 1992, 238, 325–336]. We discuss methods to identify an optimal smoothing scale ℓ and the effects of this choice on the results. From spectral analysis of the magnetic, density and velocity fields, we find a suitable smoothing length for all three fields, of . Such a smoothing scale is likely to be sensitive to the choice of simulation parameters; this may be considered in future work, but here we just explore the methodology. We discuss the properties of third-order statistical moments in fluctuations of kinetic energy density in compressible flows, and suggest their physical interpretation. The mean magnetic field, amplified by a mean-field dynamo, significantly alters the distribution of kinetic energy in space and between scales, reducing the magnitude of kinetic energy at intermediate scales. This intermediate-scale kinetic energy is a useful diagnostic of the importance of SN-driven outflows.

Global strong solution to 3D full compressible magnetohydrodynamic flows with vacuum at infinity

Global strong solution to 3D full compressible magnetohydrodynamic flows with vacuum at infinity

Theoretical analysis of quasi-one-dimensional compressible magnetohydrodynamic channel flow

A theoretical analysis of quasi-one-dimensional, steady, inviscid, compressible channel flow at a low magnetic Reynolds number with variable cross-section is performed in this paper. A second-order nonlinear dynamical system describing the variation of physical parameters is investigated in the phase plane. The characteristics of all possible channel flow with a constant electromagnetic field are obtained by the phase plane and the isomorphism of labeled graphs. It is revealed that the magnetic interaction number novelly derived from the variation rate of the cross-sectional area could significantly affect the phase trajectory in the phase plane of dimensionless velocity and Mach number. Meanwhile, the phase trajectory is only dependent on this magnetic interaction number. Further analysis of the second-order dynamical system discovers five critical values in the range of the magnetic interaction number. These five critical values can divide the whole range into eight subsets under the isomorphism of labeled graphs, forming eight equivalence classes of the phase plane. The study of such eight equivalence classes reveals that the variable cross-section flow in the phase plane can be viewed as a linear superposition of constant cross-section magnetohydrodynamic flow and isentropic flow, the weight ratio being exactly the magnetic interaction number. Consequently, for the divergent channel, the acceleration region in the supersonic zone is larger than that of the constant cross-section flow, while for the convergent channel, only the acceleration region in the subsonic zone is larger than that of the constant cross-section flow.

On global solutions to a viscous compressible two-fluid model with unconstrained transition to single-phase flow in three dimensions

We consider the Dirichlet problem for a compressible two-fluid model in multi-dimensions. It consists of the continuity equations for each fluid and the momentum equations for the mixture. This model can be derived from the compressible two-fluid model with equal velocities (Bresch et al., in Arch Rational Mech Anal 196:599–629, 2010) and from a scaling limit of the Vlasov-Fokker-Planck/compressible Navier-Stokes (Mellet and Vasseur, Commun Math Phys 281(3):573–596, 2008) (see also the compressible Oldroyd-B model with stress diffusion (Barrett et al., Commun Math Sci 15:1265–1323, 2017). Another interesting connection is that it is formally the equations of compressible magnetohydrodynamic (MHD) flows without resistivity in two dimensions under the action of vertical magnetic field (Li and Sun, J Differ Equ 267(6): 3827–3851, 2019). Under weak assumptions on the initial data which can be discontinuous, unbounded and large as well as involve transition to pure single-phase points or regions, we show existence of global weak solutions with finite energy. The essential novelty of this work, compared with previous works on the same model, is that transition to each single-phase flow is allowed without any constraints between adiabatic constants or two densities. It means that one of the phases can vanish in a point while the other can persist. The lack of enough regularity for each densities brings up essential difficulties in the two-component pressure compared with the single-phase model, i.e., compressible Navier-Stokes equations. The key points to achieve the main result rely on the variables reduction technique for the pressure function, domain separation, and some new estimates. As a byproduct, we obtain the existence of global weak solutions to the compressible MHD system without resistivity in two dimensions under the action of non-negatively vertical magnetic field, which represents a step forward to the study of the global large solution to the compressible MHD system without resistivity.

Energy conservation for the weak solutions to the 3D compressible magnetohydrodynamic equations of viscous non-resistive fluids in a bounded domain

In this paper, inspired by the work of Chen–Liang–Wang–Xu (Chen et al., 2020) on compressible Navier–Stokes equations, we obtain the energy conservation for weak solutions of the compressible non-resistive magnetohydrodynamic flows in a bounded domain Ω⊂R3. To ensure the energy conservation, we need the same regularity conditions of density and velocity as in Chen et al. (2020), moreover, H∈Lt4Lx4 and ∇H∈Ltp1Lxq1, where p1=4p3p−4, q1=4q3q−4. Under these conditions, p1∈(43,2], q1∈(43,127] when p≥4 and q≥6.

Numerical solution of compressible Euler and Magnetohydrodynamic flow past an infinite cone

A numerical scheme is developed for systems of conservation laws on manifolds which arise in high speed aerodynamics and magneto-aerodynamics. The systems are presented in an arbitrary coordinate system on the manifold and involve source terms which account for the curvature of the domain. In order for a numerical method to accurately capture the behavior of the system it is solving, the equations must be discretized in a way that is not only consistent in value, but also models the appropriate character of the system. Such a discretization is presented in this work which preserves the tensorial transformation relationships involved in formulating equations in a curved space. A numerical method is then developed and applied to the conical Euler and Ideal Magnetohydrodynamic equations. To the authors’ knowledge, this is the first demonstration of a numerical solver for the conical Ideal MHD equations. Along with the curvature of the domain, is the added challenge that both systems of equations are of mixed type. Both systems change between elliptic and hyperbolic type throughout the domain, which had to be accommodated by the numerical method.

Direct numerical simulation study on the mechanisms of the magnetic field influencing the turbulence in compressible magnetohydrodynamic flow

The magnetohydrodynamic (MHD) control has great potential in the applications of hypersonic vehicles. Typically, the MHD flowfield in these applications is low magnetic Reynolds (Rem ) compressible turbulent flow, which is different from that without magnetic field and within the high Rem range. This paper investigated the low Rem compressible MHD isotropic turbulence in different Taylor-scale Reynolds numbers and interaction parameters via the Direct Numerical Simulation (DNS), and the influence of the magnetic field on the turbulence is researched. Results indicate that the normal Reynolds stress decreases in the direction perpendicular to the magnetic field. Moreover, the eddies are stretched in the direction parallel to the magnetic field. Besides, the Joule dissipation quicken the decay of the turbulent kinetic energy, and occurs mainly in large scale vortex. Based on the DNS data, the correlation between fluctuating electric intensity and velocity is studied. Results indicate that the electric intensity agrees well with the first-order approximate solution of the electric potential equation. Accordingly, an improved closure model of the correlation terms is established, where a coefficient related to the local turbulent Mach number is proposed. Comparisons with the DNS results reveal that the proposed model could correctly predict the correlation terms.

Optimal time‐decay rates for the 3D compressible Magnetohydrodynamic flows with discontinuous initial data and large oscillations

Optimal time‐decay rates for the 3D compressible Magnetohydrodynamic flows with discontinuous initial data and large oscillations