A mimetic finite difference based quasi-static magnetohydrodynamic solver for force-free plasmas in tokamak disruptions

Force-free plasmas are a good approximation where the plasma pressure is tiny compared with the magnetic pressure, which is the case during the cold vertical displacement event (VDE) of a major disruption in a tokamak. On time scales long compared with the transit time of Alfven waves, the evolution of a force-free plasma is most efficiently described by the quasi-static magnetohydrodynamic (MHD) model, which ignores the plasma inertia. Here we consider a regularized quasi-static MHD model for force-free plasmas in tokamak disruptions and propose a mimetic finite difference (MFD) algorithm. The full geometry of an ITER-like tokamak reactor is treated, with a blanket module region, a vacuum vessel region, and the plasma region. Specifically, we develop a parallel, fully implicit, and scalable MFD solver based on PETSc and its DMStag data structure for the discretization of the five-field quasi-static perpendicular plasma dynamics model on a 3D structured mesh. The MFD spatial discretization is coupled with a fully implicit DIRK scheme. The algorithm exactly preserves the divergence-free condition of the magnetic field under the resistive Ohm's law. The preconditioner employed is a four-level fieldsplit preconditioner, which is created by combining separate preconditioners for individual fields, that calls multigrid or direct solvers for sub-blocks or exact factorization on the separate fields. The numerical results confirm the divergence-free constraint is strongly satisfied and demonstrate the performance of the fieldsplit preconditioner and overall algorithm. The simulation of ITER VDE cases over the actual plasma current diffusion time is also presented.Comment: 43 page

A New Conservative Remap Method for Discontinuous Numerical Fields

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NUMERICAL METHODS FOR SOLUTION OF HELMHOLTZ's WAVE EQUATION

The work covers the numerical methods for solution of the problems connected with scattering of the monochromatic acoustic waves by the composite obstacles with piecewise-constant characteristics. The aim is to develop the numerical methods and to create the software for solving problems of the scattering in case of the high frequencies and large jump of the coefficients. The numerical stability in the new method for approximation of the Sommerfeld's radiation conditions has been proved. The approximated method for decomposition of the field for two-dimensional problems with large jump of the coefficients has been proposed. The program complexes for solving two- and three-dimensional problems of the scattering in case of the complex shape scattering obstacles have been developed. The efficiency of using the absorbing boundary conditions in the method of forged components for solving three-dimensional problems of the acoustics in the field of the high frequencies has been confirmed in experimentAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio

Domain Decomposition with Subdomain CCG for Material Jump Elliptic Problems

A combination of the cascadic conjugate gradient (CCG) method for homogeneous problems with a non-overlapping domain decomposition (DD) method is studied. Mortar finite elements on interfaces are applied to permit nonmatching grids in neighboring subdomains. For material jump problems, the method is designed as an alternative to the cascadic methods. 1 Introduction In this paper we consider linear elliptic problems #(a#u) + cu = f on general domains with space dimension p equal to 2 or 3, where typically the coe#cient a is strongly varying. This type of problems arises whenever di#erent materials are combined. Standard (multiplicative) multigrid methods [13] or additive multilevel methods such as KASKADE with BPX preconditioners [12, 20, 9] deal quite e#ciently with such a situation - apart from certain pathological examples in 3D. However, the recently developed cascadic multigrid methods such as CCG [11, 8, 7, 6], which are extremely fast for homogeneous problems, tend to exhi..

Multidimensional Staggered Grid Residual Distribution Scheme for Lagrangian Hydrodynamics

We present the second-order multidimensional staggered grid hydrodynamics residual distribution (SGH RD) scheme for Lagrangian hydrodynamics. The SGH RD scheme is based on the staggered finite element discretizations as in [V. A. Dobrev, T. V.Kolev, and R. N. Rieben, SIAM J. Sci. Comput. 34 (2012), pp. B606--B641]. However, the advantage of the residual formulation over classical FEM approaches consists in the natural mass matrix diagonalization which allows one to avoid the solution of the linear system with the global sparse mass matrix while retaining the desired order of accuracy. This is achieved by using Bernstein polynomials as finite element shape functions and coupling the space discretization with the deferred correction type timestepping method. Moreover, it can be shown that for the Lagrangian formulation written in nonconservative form, our RD scheme ensures the exact conservation of the mass, momentum, and total energy. In this paper, we also discuss construction of numerical viscosity approximations for the SGH RD scheme, allowing us to reduce the dissipation of the numerical solution. Thanks to the generic formulation of the staggered grid RD scheme, it can be directly applied to both single- and multimaterial and multiphase models. Finally, we demonstrate computational results obtained with the proposed RD scheme for several challenging test problems

The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods

The objective of the Arbitrary Lagrangian-Eulerian (ALE) methodology for solving multidimensional fluid flow problems is to move the computational mesh, using the flow as a guide, to improve the robustness, accuracy and efficiency of a simulation. The main elements in the ALE simulation are an explicit Lagrangian phase, a rezone phase in which a new mesh is defined, and a remapping (conservative interpolation) phase, in which the Lagrangian solution is transferred to the new mesh. In most ALE codes, the main goal of the rezone phase is to maintain high quality of the rezoned mesh. In this article, we describe a new rezone strategy which minimizes the L 2 norm of the solution error and maintains smoothness of the mesh. The efficiency of the new method is demonstrated with numerica