Implicit adaptive grid plasma simulation

In a plasma simulation, the nonlinear interactions among the charged particles and the fields they generate are calculated by solving particle equations of motion self- consistently with Maxwell`s equations. Standard methods simulate plasmas by solving explicit approximations to the equations of motion with a representative sample of charged particles. Explicit methods must resolve all time scales, including the fastest, the electron plasma oscillations, for numerical stability. Because plasmas exhibit a wide range of natural frequencies, ranging from electromagnetic waves and electron plasma oscillations at high frequencies, to sound waves and mass motion at low frequency, it is clearly impossible to ,cover this range of length and time scales with a small time step. Reduced equations, such as the gyrokinetic model, the hybrid model, or the {delta}f method remove the most restrictive constraints on the time step by removing some of the physics. Implicit methods, remove this constraint by giving unconditional stability. With the implicit formulation, one can choose the time step to resolve the time scale of interest, rather than restrict the time step to a small value to maintain numerical stability. The two basic implicit formulations, the direct and implicit moment methods, also reduce the cost by reducing the number of equations that must be solved, but differently from the hybrid method. The direct method extrapolates particle motion forward in time along unperturbed particle orbits, and the implicit moment method calculates the fields in which the particles move by solving coupled field and moment equations self-consistently. Closure is given by data from the simulation particles. Both the direct and implicit moment methods give accurate estimates of the evolution of the charge and current density when the (electron) particle displacement per time step is smaller than the grid spacing

Relationships between a roller and a dynamic pressure distribution in circular hydraulic jumps

We investigated numerically the relation between a roller and the pressure distribution to clarify the dynamics of the roller in circular hydraulic jumps. We found that a roller which characterizes a type II jump is associated with two high pressure regions after the jump, while a type I jump (without the roller) is associated with only one high pressure region. Our numerical results show that building up an appropriate pressure field is essential for a roller.Comment: 10 pages, 7 PS files. To appear in PR

Higher order finite difference schemes for the magnetic induction equations

We describe high order accurate and stable finite difference schemes for the initial-boundary value problem associated with the magnetic induction equations. These equations model the evolution of a magnetic field due to a given velocity field. The finite difference schemes are based on Summation by Parts (SBP) operators for spatial derivatives and a Simultaneous Approximation Term (SAT) technique for imposing boundary conditions. We present various numerical experiments that demonstrate both the stability as well as high order of accuracy of the schemes.Comment: 20 page

On the dispersion of solid particles in a liquid agitated by a bubble swarm

This article deals with the dispersion of solid particles in a liquid agitated by a homogeneous swarm of bubbles. The scale of interest lies between the plant scale (of the order of the tank) and the microscale (less than the bubble diameter). The strategy consists in simulating both the twophase flow of deforming bubbles and the motion of solid particles. The evolution of the spatial distribution of particles together with the encounter and entrainment phenomena is studied as a function of the void fraction and the relative size and mass of particles. The influence of the shape of the bubble and of the model of forces that govern the motion of particles is also considered

Implementation of a flexible and modular multiphase framework for the analysis of surface-tension-driven flows based on a LS-VOF approach

The mathematical modelling and numerical simulation of multi-phase flows are both a demanding and highly complex exercise. In typical problems with industrial relevance, the fluids are often in non-isothermal conditions and interfacial phenomena are a relevant part of the problem. A number of effects due to the presence of temperature differences must be adequately taken into account to make the results of numerical simulations consistent and realistic. Moreover, in general, gradients of surface tension at the interface separating two liquids are a source of numerical issues that can delay (and even prevent completely in some circumstances) the convergence of the solution algorithm. Here, we propose a fundamental and concerted approach for the simulation of the typical dynamics resulting from the presence of a dispersed phase in an external matrix in nonisothermal conditions based on the modular computer-aided design, modelling, and simulations capabilities of the OpenFOAM environment. The resulting framework is tested against the migration of a droplet induced by thermocapillary effects in the absence of gravity. The simulations are fully three-dimensional and based on an adaptive mesh refinement (AMR) strategy. We describe in detail the countermeasures taken to circumvent the problematic issues associated with the simulation of this kind of flows

Modeling on fluid flow and inclusion motion in centrifugal continuous casting strands

During the centrifugal continuous casting process, unreasonable casting parameters can cause violent level fluctuation, serious gas entrainment, and formation of frozen shell pieces at the meniscus. Thus, in the current study, a three-dimensional multiphase turbulent model was established to study the transport phenomena during centrifugal continuous casting process. The effects of nozzle position, casting and rotational speed on the flow pattern, centrifugal force acting on the molten steel, level fluctuation, gas entrainment, shear stress on mold wall, and motion of inclusions during centrifugal continuous casting process were investigated. Volume of Fluid model was used to simulate the molten steel-air two-phase. The level fluctuation and the gas entrainment during casting were calculated by user-developed subroutines. The trajectory of inclusions in the rotating system was calculated using the Lagrangian approach. The results show that during centrifugal continuous casting, a large amount of gas was entrained into the molten steel, and broken into bubbles of various sizes. The greater the distance to the mold wall, the smaller the centrifugal force. Rotation speed had the most important influence on the centrifugal force distribution at the side region. Angular moving angle of the nozzle with 8° and keeping the rotation speed with 60 revolutions per minute can somehow stabilize the level fluctuation. The increase of angular angle of nozzle from 8 to 18 deg and rotation speed from 40 to 80 revolutions per minute favored to decrease the total volume of entrained bubbles, while the increase of distance of nozzle moving left and casting speed had reverse effects. The trajectories of inclusions in the mold were irregular, and then rotated along the strand length. After penetrating a certain distance, the inclusions gradually moved to the center of billet and gathered there. More work, such as the heat transfer, the solidification, and the inclusions entrapment during centrifugal continuous casting, will be performed