There are many interesting physical processes which involve the generation of high density plasmas in large volumes. However, when modeling these systems numerically, the large densities and volumes present a significant computational challenge. One technique for modeling plasma physics, the particle in cell (PIC) approach, is very accurate but requires increasing computation time and numerical resolution as the density of the plasma grows. In this paper we present a new technique for mitigating the extreme computational load as the plasma density grows by combining existing PIC methods with a dielectric fluid approach. By using both descriptions in a hybrid particle-fluid model, we now can probe the physics in large volume, high density regions. The hybrid method also provides a smooth transition as the plasma density increases and the ionization fraction grows to values that are well described by the fluid description alone. We present the hybrid technique and demonstrate the validity of the physical model by benchmarking against a simple example with an analytic solution.
We describe gas dynamic and plasma effects for transient plasma jets under different conditions. Our Unified Flow Solver (UFS) is evaluated for simulations of mixed continuum-rarefied flows, transient gas expansion dynamics and collisionless plasma expansion. We identify further advances that are required for hybrid fluid-kinetic simulations of laser-ablation and EEE-induced plasma jets.
Immersed boundary methods for computing confined fluid and plasma flows in complex geometries are reviewed. The mathematical principle of the volume penalization technique is described and simple examples for imposing Dirichlet and Neumann boundary conditions in one dimension are given. Applications for fluid and plasma turbulence in two and three space dimensions illustrate the applicability and the efficiency of the method in computing flows in complex geometries, for example in toroidal geometries with asymmetric poloidal cross-sections.
The document describes a numerical algorithm for plasms and fluids by the Lagrange method, in which the spatial meshes follow the plasma and fluid behavior. Through the mesh wall the plasma and the fluid do not escape. The 3D Lagrange code is originally designed to simulate a Gold cone plasma, which is relevant to confine an imploding fuel in the cone in inertial confinement fusion. However, the 3D Lagrange code would be applied to simulate plasmas and fluids, which are not deformed seriously. The 3D code is designed in the spatial Cartesian coordinate (x, y, z), and employs the compressible f…
We present a solver of 3D two-fluid plasma model for the simulation of short-pulse laser interactions with plasma. This solver resolves the equations of the two-fluid plasma model with ideal gas closure. We also include the Bhatnagar-Gross-Krook collision model. Our solver is based on PseudoSpectral Time-Domain (PSTD) method to solve Maxwell's curl equations. We use a Strang splitting to integrate Euler equations with source term: while Euler equations are solved with a composite scheme mixing Lax-Friedrichs and Lax-Wendroff schemes, the source term is integrated with a fourth-order Runge-Kutt…
The closure problem in fluid modeling is a well-known challenge to modelers aiming to accurately describe their system of interest. Over many years, analytic formulations in a wide range of regimes have been presented but a practical, generalized fluid closure for magnetized plasmas remains an elusive goal. In this study, as a first step towards constructing a novel data based approach to this problem, we apply ever-maturing machine learning methods to assess the capability of neural network architectures to reproduce crucial physics inherent in popular magnetized plasma closures. We find enco…
A new global two-fluid electromagnetic turbulence code, CENTORI, has been developed for the purpose of studying magnetically-confined fusion plasmas on energy confinement timescales. This code is used to evolve the combined system of electron and ion fluid equations and Maxwell equations in toroidal configurations with axisymmetric equilibria. Uniquely, the equilibrium is co-evolved with the turbulence, and is thus modified by it. CENTORI is applicable to tokamaks of arbitrary aspect ratio and high plasma beta. A predictor-corrector, semi-implicit finite difference scheme is used to compute th…
Drift-diffusion plasma fluid models are commonly used to simulate electric discharges. Such models can computationally be very efficient if they are combined with explicit time integration. This paper deals with two issues that often arise with such models. First, a high plasma conductivity can severely limit the time step. A fully explicit method to overcome this limitation is presented. This method is compared to the existing semi-implicit method, and it is shown to have several advantages. A second issue is specific to models with the local field approximation. Near strong density and elect…
Recently the drift-reduced Landau fluid six-field turbulence model within the BOUT++ framework has been upgraded. In particular, this new model employs a new normalization, adds a volumetric flux-driven source option, the Landau fluid closure for parallel heat flux and a Laplacian inversion solver which is able to capture n=0 axisymmetric mode evolution in realistic tokamak configurations. These improvements substantially extended model's capability to study a wider range of tokamak edge phenomena, and are essential to build a fully self-consistent edge turbulence model capable of both transie…
A massively parallel simulation code, called \textit{dHybrid}, has been developed to perform global scale studies of space plasma interactions. This code is based on an explicit hybrid model; the numerical stability and parallel scalability of the code are studied. A stabilization method for the explicit algorithm, for regions of near zero density, is proposed. Three-dimensional hybrid simulations of the interaction of the solar wind with unmagnetized artificial objects are presented, with a focus on the expansion of a plasma cloud into the solar wind, which creates a diamagnetic cavity and dr…
We present a new multi-fluid, multi-temperature plasma solver with adaptive Cartesian mesh (ACM) based on a full-Newton (non-linear, implicit) scheme for collisional low-temperature plasma. The particle transport is described using the drift-diffusion approximation for electrons and ions coupled to Poisson equation for electric field. In addition, the electron-energy transport equation is solved to account for electron thermal conductivity, Joule heating, and energy loss of electrons in collisions with neutral species. The rate of electron-induced ionization is a function of electron temperatu…
A new method that solves concurrently the multi-fluid and Maxwell's equations has been developed for plasma simulations. By calculating the stress tensor in the multi-fluid momentum equation by means of computational particles moving in a self-consistent electromagnetic field, the kinetic effects are retained while solving the multi-fluid equations. The Maxwell's and multi-fluid equations are discretized implicitly in time enabling kinetic simulations over time scales typical of the fluid simulations. The fluid-kinetic Particle-in-Cell solver has been implemented in a three-dimensional electro…
A discontinuous Galerkin method for the ideal 5 moment two-fluid plasma system is presented. The method uses a second or third order discontinuous Galerkin spatial discretization and a third order TVD Runge-Kutta time stepping scheme. The method is benchmarked against an analytic solution of a dispersive electron acoustic square pulse as well as the two-fluid electromagnetic shock and existing numerical solutions to the GEM challenge magnetic reconnection problem. The algorithm can be generalized to arbitrary geometries and three dimensions. An approach to maintaining small gauge errors based …
Recently, J. Teunissen reported a fully explicit method, namely the current-limit approach, which claimed to overcome the dielectric relaxation time restriction for the drift-diffusion plasma fluid model. In this comment, we point out that the current-limit approach is not mathematically consistent, and discuss about the possible reason why the inconsistency was not visibly noticed.
A general dispersion-relation solver that numerically evaluates the full propagation properties of all the waves in fluid plasmas is presented. The effects of anisotropic pressure, external magnetic fields and beams, relativistic dynamics, as well as local plasma inhomogeneity are included. [Computer Physics Communications, (2013); doi: 10.1016/j.cpc.2013.10.012; code: http://cpc.cs.qub.ac.uk/summaries/AERF\_v1\_0.html]
We investigate the performance of a hybrid plasma solver on the test problem of an ion beam. The parallel solver is based on cell centered finite differences in space, and a predictor-corrector leapfrog scheme in time. The implementation is done in the FLASH software framework. It is shown that the solver conserves energy well over time, and that the parallelization is efficient (it exhibits weak scaling).
In this paper we present a new three dimensional (3D) full electromagnetic relativistic hybrid plasma code H-VLPL (hybrid virtual laser plasma laboratory). The full kinetic particle-in-cell (PIC) method is used to simulate low density hot plasmas while the hydrodynamic model applies to the high density cold background plasma. To simulate the linear electromagnetic response of the high density plasma, we use a newly developed form of an exponential integrator method. It allows us to simulate plasmas of arbitrary densities using large time steps. The model reproduces the plasma dispersion and gi…
A key uncertainty in the design and development of magnetic confinement fusion energy reactors is predicting edge plasma turbulence. An essential step in overcoming this uncertainty is the validation in accuracy of reduced turbulent transport models. Drift-reduced Braginskii two-fluid theory is one such set of reduced equations that has for decades simulated boundary plasmas in experiment, but significant questions exist regarding its predictive ability. To this end, using a novel physics-informed deep learning framework, we demonstrate the first ever direct quantitative comparisons of turbule…
The document describes a numerical algorithm to simulate plasmas and fluids in the 3 dimensional space by the Euler method, in which the spatial meshes are fixed to the space. The plasmas and fluids move through the spacial Euler mesh boundary. The Euler method can represent a large deformation of the plasmas and fluids. On the other hand, when the plasmas or fluids are compressed to a high density, the spatial resolution should be ensured to describe the density change precisely. The present 3D Euler code is developed to simulate a nuclear fusion fuel ignition and burning. Therefore, the 3D E…
Heliospheric plasmas require multi-scale and multi-physics considerations. On one hand, MHD codes are widely used for global simulations of the solar-terrestrial environments, but do not provide the most elaborate physical description of space plasmas. Hybrid codes, on the other hand, capture important physical processes, such as electric currents and effects of finite Larmor radius, but they can be used locally only, since the limitations in available computational resources do not allow for their use throughout a global computational domain. In the present work, we present a new coupled sche…
We describe recent developments in the hybrid atomistic/continuum modelling of dense fluids. We discuss the general implementation of mass, momentum and energy transfers between a region described by molecular dynamics and the neighbouring domain described by the Navier-Stokes equations for unsteady flow. The effect of fluctuations from the particle system in the scheme accuracy is also studied.
We review a scalable two- and three-dimensional computer code for low-temperature plasma simulations in multi-material complex geometries. Our approach is based on embedded boundary (EB) finite volume discretizations of the minimal fluid-plasma model on adaptive Cartesian grids, extended to also account for charging of insulating surfaces. We discuss the spatial and temporal discretization methods, and show that the resulting overall method is second order convergent, monotone, and conservative (for smooth solutions). Weak scalability with parallel efficiencies over 70\% are demonstrated up to…
In this paper, we propose a hybrid lattice Boltzmann method (HLBM) for solving fluid-structure interaction problems. The proposed numerical approach is applied to model the flow induced by a vibrating thin lamina submerged in a viscous quiescent fluid. The hydrodynamic force exerted by the fluid on the solid body is described by means of a complex hydrodynamic function, whose real and imaginary parts are determined via parametric analysis. Numerical results are validated by comparison with those from other numerical as well as experimental works available in the literature. The proposed hybrid…
