Current Coupling Scheme Research Articles

Coupling multi-fluid dynamics equipped with Landau closures to the particle-in-cell method

The particle-in-cell (PIC) method is successfully used to study magnetized plasmas. However, this requires large computational costs and limits simulations to short physical run times and often to set-ups of less than three spatial dimensions. Traditionally, this is circumvented either via hybrid-PIC methods (adopting massless electrons) or via magneto-hydrodynamic-PIC methods (modelling the background plasma as a single charge-neutral magneto-hydrodynamical fluid). Because both methods preclude modelling important plasma-kinetic effects, we introduce a new fluid-PIC code that couples a fully explicit and charge-conserving multi-fluid solver to the PIC code SHARP through a current-coupling scheme and solve the full set of Maxwell's equations. This avoids simplifications typically adopted for Ohm's law and enables us to fully resolve the electron temporal and spatial scales while retaining the versatility of initializing any number of ion, electron or neutral species with arbitrary velocity distributions. The fluid solver includes closures emulating Landau damping so that we can account for this important kinetic process in our fluid species. Our fluid-PIC code is second-order accurate in space and time. The code is successfully validated against several test problems, including the stability and accuracy of shocks and the dispersion relation and damping rates of waves in unmagnetized and magnetized plasmas. It also matches growth rates and saturation levels of the gyro-scale and intermediate-scale instabilities driven by drifting charged particles in magnetized thermal background plasmas in comparison with linear theory and PIC simulations. This new fluid-SHARP code is specially designed for studying high-energy cosmic rays interacting with thermal plasmas over macroscopic time scales.

Meta-coupler arrays linking propagating waves and photonic topological modes on a chip.

Photonic topological modes (PTMs) have attracted increasing attention due to their robust optical performance, which provides a defect-tolerant strategy for chip-integrated photonic systems. The current coupling schemes rely on bulky structures that severely limit their potential applications in high-density optical integration. Here, plasmonic metasurfaces loaded on topological waveguide arrays are explored to generate PTMs. The normally incident circularly polarized beam can be coupled into the topological interface or edge modes after carefully optimizing the metasurfaces. The result provides a compact and flexible method for PTMs generation on a chip, suggesting a promising avenue toward the application of topological photonic devices.

Hybrid simulation of energetic particles interacting with magnetohydrodynamics using a slow manifold algorithm and GPU acceleration

The hybrid method combining particle-in-cell and magnetohydrodynamics can be used to study the interaction between energetic particles and global plasma modes. In this paper we introduce the M3D-C1-K code, which is developed based on the M3D-C1 finite element code solving the magnetohydrodynamics equations, with a newly developed kinetic module simulating energetic particles. The particle pushing is done using a new algorithm by applying the Boris pusher to the classical Pauli particles to simulate the slow-manifold of particle orbits, with long-term accuracy and fidelity. The particle pushing can be accelerated using GPUs with a significant speedup. The moments of the particles are calculated using the δf method, and are coupled into the magnetohydrodynamics simulation through pressure or current coupling schemes. Several linear simulations of magnetohydrodynamics modes driven by energetic particles have been conducted using M3D-C1-K with the δf method, including fishbone, toroidal Alfvén eigenmodes and reversed shear Alfvén eigenmodes. Good agreement with previous results from other eigenvalue, kinetic and hybrid codes have been achieved.

Hamiltonian kinetic-Hall magnetohydrodynamics with fluid and kinetic ions in the current and pressure coupling schemes

We present two generalized hybrid kinetic-Hall magnetohydrodynamics (MHD) models describing the interaction of a two-fluid bulk plasma, which consists of thermal ions and electrons, with energetic, suprathermal ion populations described by Vlasov dynamics. The dynamics of the thermal components are governed by standard fluid equations in the Hall MHD limit with the electron momentum equation providing an Ohm's law with Hall and electron pressure terms involving a gyrotropic electron pressure tensor. The coupling of the bulk, low-energy plasma with the energetic particle dynamics is accomplished through the current density (current coupling scheme; CCS) and the ion pressure tensor appearing in the momentum equation (pressure coupling scheme; PCS) in the first and the second model, respectively. The CCS is a generalization of two well-known models, because in the limit of vanishing energetic and thermal ion densities, we recover the standard Hall MHD and the hybrid kinetic-ions/fluid-electron model, respectively. This provides us with the capability to study in a continuous manner, the global impact of the energetic particles in a regime extending from vanishing to dominant energetic particle densities. The noncanonical Hamiltonian structures of the CCS and PCS, which can be exploited to study equilibrium and stability properties through the energy-Casimir variational principle, are identified. As a first application here, we derive a generalized Hall MHD Grad–Shafranov–Bernoulli system for translationally symmetric equilibria with anisotropic electron pressure and kinetic effects owing to the presence of energetic particles using the PCS.

MHD-kinetic hybrid code based on structure-preserving finite elements with particles-in-cell

We present a STRUcture-Preserving HYbrid code - STRUPHY - for the simulation of magneto-hydrodynamic (MHD) waves interacting with a population of energetic particles far from thermal equilibrium (kinetic species). The implemented model features linear, ideal MHD equations in curved, three-dimensional space, coupled nonlinearly to the full-orbit Vlasov equations via a current coupling scheme. The algorithm is based on finite element exterior calculus (FEEC) for MHD and particle-in-cell (PIC) methods for the kinetic part; it provably conserves mass, energy, and the divergence-free magnetic field, irrespective of metric (= space curvature), mesh parameters and chosen order of the scheme. These properties enable reliable long-time simulations of energetic particle physics in complex geometries, covering the whole range of MHD waves. In STRUPHY, the finite element spaces are built from tensor products of univariate B-splines on the logical cuboid and can be made high-order by increasing the polynomial degree. Time-stepping is based on a skew-symmetric splitting with implicit sub-steps, mitigating CFL conditions from fast magneto-acoustic waves. High-order time splitting schemes can be used in this regard.

A 3D unstructured grid nearshore hydrodynamic model based on the vortex force formalism

A new three-dimensional nearshore hydrodynamic model system is developed based on the unstructured-grid version of the third generation spectral wave model SWAN (Un-SWAN) coupled with the three-dimensional ocean circulation model FVCOM to enable the full representation of the wave-current interaction in the nearshore region. A new wave–current coupling scheme is developed by adopting the vortex-force (VF) scheme to represent the wave–current interaction. The GLS turbulence model is also modified to better reproduce wave-breaking enhanced turbulence, together with a roller transport model to account for the effect of surface wave roller. This new model system is validated first against a theoretical case of obliquely incident waves on a planar beach, and then applied to three test cases: a laboratory scale experiment of normal waves on a beach with a fixed breaker bar, a field experiment of oblique incident waves on a natural, sandy barred beach (Duck’94 experiment), and a laboratory study of normal-incident waves propagating around a shore-parallel breakwater. Overall, the model predictions agree well with the available measurements in these tests, illustrating the robustness and efficiency of the present model for very different spatial scales and hydrodynamic conditions. Sensitivity tests indicate the importance of roller effects and wave energy dissipation on the mean flow (undertow) profile over the depth. These tests further suggest to adopt a spatially varying value for roller effects across the beach. In addition, the parameter values in the GLS turbulence model should be spatially inhomogeneous, which leads to better prediction of the turbulent kinetic energy and an improved prediction of the undertow velocity profile.

Variational approach to low-frequency kinetic-MHD in the current coupling scheme

Hybrid kinetic-MHD models describe the interaction of an MHD bulk fluid with an ensemble of hot particles, which obeys a kinetic equation. In this work we apply Hamilton’s variational principle to formulate new current-coupling kinetic-MHD models in the low-frequency approximation (i.e. large Larmor frequency limit). More particularly, we formulate current-coupling schemes, in which energetic particle dynamics are expressed in either guiding center or gyrocenter coordinates. When guiding center theory is used to model the hot particles, we show how energy conservation requires corrections to the standard magnetization term. On the other hand, charge and momentum conservation in gyrokinetic-MHD lead to extra terms in the usual definition of the hot current density as well as modifications to conventional gyrocenter dynamics. All these new features arise naturally from the underlying variational structure of the proposed models.

Particulate Immersed Boundary Method for complex fluid–particle interaction problems with heat transfer

In our recent work (Zhang et al., 2015), a Particulate Immersed Boundary Method (PIBM) for simulating fluid-particle multiphase flow was proposed and assessed in both two- and three-dimensional applications. In this study, the PIBM was extended to solve thermal interaction problems between spherical particles and fluid. The Lattice Boltzmann Method (LBM) was adopted to solve the fluid flow and temperature fields, the PIBM was responsible for the no-slip velocity and temperature boundary conditions at the particle surface, and the kinematics and trajectory of the solid particles were evaluated by the Discrete Element Method (DEM). Four case studies were implemented to demonstrate the capability of the current coupling scheme. Firstly, numerical simulation of natural convection in a two-dimensional square cavity with an isothermal concentric annulus was carried out for verification purpose. The current results were found to have good agreement with previous references. Then, sedimentation of two-and three-dimensional isothermal particles in fluid was numerically studied, respectively. The instantaneous temperature distribution in the cavity was captured. The effect of the thermal buoyancy on particle behaviors was discussed. Finally, sedimentation of three-dimensional thermosensitive particles in fluid was numerically investigated. Our results revealed that the LBM–PIBM–DEM is a promising scheme for the solution of complex fluid–particle interaction problems with heat transfer.

A combined TLBM–IBM–DEM scheme for simulating isothermal particulate flow in fluid

A combined Thermal Lattice Boltzmann Method (TLBM) – Immersed Boundary Method (IBM) – Discrete Element Method (DEM) scheme was proposed to simulate fluid–particle multiphase flows with heat transfer. The coupling scheme could be regarded as a natural next step of our recent work (Zhang et al., 2014). Here, we enabled an additional function to treat heat transfer problems based on the original LBM–IBM–DEM scheme without introducing any artificial parameters. Firstly, sedimentation of one and two isothermal particles in fluid was numerically investigated, respectively. The feature of instantaneous temperature distribution was captured. The effect of thermal buoyancy on the particle behavior was discussed. Obtained numerical results showed good agreements with previous studies. Then, another two cases involving a large number of isothermal particles were further implemented to demonstrate the capability of current coupling scheme. The numerical results revealed that the TLBM–IBM–DEM is a promising scheme for the solution of complex fluid–particle interaction problems with heat transfer.

Euler-Poincaré formulation of hybrid plasma models

Three different hybrid Vlasov-fluid systems are derived by applying reduction by symmetry to Hamilton's variational principle. In particular, the discussion focuses on the Euler-Poincar\'e formulation of three major hybrid MHD models, which are compared in the same framework. These are the current-coupling scheme and two different variants of the pressure-coupling scheme. The Kelvin-Noether theorem is presented explicitly for each scheme, together with the Poincar\'e invariants for its hot particle trajectories. Extensions of Ertel's relation for the potential vorticity and for its gradient are also found in each case, as well as new expressions of cross helicity invariants.

The QM‐MM interface for CHARMM‐deMon

We present a new QM/MM interface for fast and efficient simulations of organic and biological molecules. The CHARMM/deMon interface has been developed and tested to perform minimization and atomistic simulations for multi-particle systems. The current features of this QM/MM interface include readability for molecular dynamics, tested compatibility with Free Energy Perturbation simulations (FEP) using the dual topology/single coordinate method. The current coupling scheme uses link atoms, but further extensions of the code to incorporate other available schemes are planned. We report the performance of different levels of theory for the treatment of the QM region, while the MM region was represented by a classical force-field (CHARMM27) or a polarizable force-field based on a simple Drude model. The current QM/MM implementation can be coupled to the dual-thermostat method and the VV2 integrator to run molecular dynamics simulations.