Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMultigrid solver for axisymmetrical 2D fluid equations
122
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We have developed an efficient algorithm for steady axisymmetrical 2D fluid equations. The algorithm employs multigrid method as well as standard implicit discretization schemes for systems of partial differential equations. Linearity of the multigrid method with respect to the number of grid points allowed us to use $256times 256$ grid, where we could achieve solutions in several minutes. Time limitations due to nonlinearity of the system are partially avoided by using multi level grids(the initial solution on $256times 256$ grid was extrapolated steady solution from $128times 128$ grid which allowed using long integration time steps). The fluid solver may be used as the basis for hybrid codes for DC discharges.
rate research
Read More
In this work, we propose and compare four different strategies to simulate the fluid model for streamer propagation in one-dimension (1D) and quasi two-dimension (2D), which consists of a Poissons equation for particle velocity and two continuity equations for particle transport. Each strategy involves of one method for solving Poissons equation and the other for solving continuity equations, and a total variation diminishing three-stage Runge-Kutta method in temporal discretization. The numerical methods for Poissons equation include finite volume method, discontinuous Galerkin methods, mixed finite element method and least-squared finite element method. The numerical method for continuity equations is chosen from the family of discontinuous Galerkin methods. The accuracy tests and comparisons show that all of these four strategies are suitable and competitive in streamer simulations from the aspects of accuracy and efficiency. Results show these methods are compatible. By applying any strategy in real simulations, we can study the dynamics of streamer propagations in both 1D and quasi 2D models.
We develop a nonlinear multigrid method to solve the steady state of microflow, which is modeled by the high order moment system derived recently for the steady-state Boltzmann equation with ES-BGK collision term. The solver adopts a symmetric Gauss-Seidel iterative scheme nested by a local Newton iteration on grid cell level as its smoother. Numerical examples show that the solver is insensitive to the parameters in the implementation thus is quite robust. It is demonstrated that expected efficiency improvement is achieved by the proposed method in comparison with the direct time-stepping scheme.
A new modular code called BOUT++ is presented, which simulates 3D fluid equations in curvilinear coordinates. Although aimed at simulating Edge Localised Modes (ELMs) in tokamak X-point geometry, the code is able to simulate a wide range of fluid models (magnetised and unmagnetised) involving an arbitrary number of scalar and vector fields, in a wide range of geometries. Time evolution is fully implicit, and 3rd-order WENO schemes are implemented. Benchmarks are presented for linear and non-linear problems (the Orszag-Tang vortex) showing good agreement. Performance of the code is tested by scaling with problem size and processor number, showing efficient scaling to thousands of processors. Linear initial-value simulations of ELMs using reduced ideal MHD are presented, and the results compared to the ELITE linear MHD eigenvalue code. The resulting mode-structures and growth-rate are found to be in good agreement (BOUT++ = 0.245, ELITE = 0.239). To our knowledge, this is the first time dissipationless, initial-value simulations of ELMs have been successfully demonstrated.
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 Euler code includes the DT fuel reactions, the alpha particle diffusion, the alpha particle deposition to heat the DT fuel and the DT fuel depletion by the DT reactions, as well as the thermal energy diffusion based on the three-temperature compressible fluid model.
A fusion boundary-plasma domain is defined by axisymmetric magnetic surfaces where the geometry is often complicated by the presence of one or more X-points; and modeling boundary plasmas usually relies on computational grids that account for the magnetic field geometry. The new grid generator INGRID (Interactive Grid Generator) presented here is a Python-based code for calculating grids for fusion boundary plasma modeling, for a variety of configurations with one or two X-points in the domain. Based on a given geometry of the magnetic field, INGRID first calculates a skeleton grid which consists of a small number of quadrilateral patches; then it puts a subgrid on each of the patches, and joins them in a global grid. This domain partitioning strategy makes possible a uniform treatment of various configurations with one or two X-points in the domain. This includes single-null, double-null, and other configurations with two X-points in the domain. The INGRID design allows generating grids either interactively, via a parameter-file driven GUI, or using a non-interactive script-controlled workflow. Results of testing demonstrate that INGRID is a flexible, robust, and user-friendly grid-generation tool for fusion boundary-plasma modeling.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
