A dynamically adaptive multigrid algorithm for the incompressible Navier-Stokes equations: Validation and model problems

An algorithm is described for the solution of the laminar, incompressible Navier-Stokes equations. The basic algorithm is a multigrid based on a robust, box-based smoothing step. Its most important feature is the incorporation of automatic, dynamic mesh refinement. This algorithm supports generalized simple domains. The program is based on a standard staggered-grid formulation of the Navier-Stokes equations for robustness and efficiency. Special grid transfer operators were introduced at grid interfaces in the multigrid algorithm to ensure discrete mass conservation. Results are presented for three models: the driven-cavity, a backward-facing step, and a sudden expansion/contraction

Improved error estimates for the perturbed Galerkin method applied to a class of generalized eigenvalue problems

AbstractWe consider the generalized eigenvalue problem x-Kx = μBx in a complex Banach space E. Here, K and B are bounded linear operators, B is compact, and 1 is not in the spectrum of K. If {En: n = 1, 2,…} is a sequence of closed subspaces of E and Pn: E → En is a linear projection which maps E onto En, then we consider the sequence of approximate eigenvalue problems {xn-PnKxn = μPnBxn in En: n = 1, 2,…}. Assuming that ‖K-PnK‖ → 0 and ‖B-PnB‖ → 0 as n → ∞, we prove the convergence of sequences of eigenvalues and eigenelements of the approximate eigenvalue problem to eigenvalues and eigenelements of the original eigenvalue problem, and establish upper bounds for the errors. These error bounds are sharper than those given by Vainikko in Ref. 2 for the more general problem x = μTx in E, T linear and compact, and the sequence of approximate problems {xn = μTnxn in En: n=l, 2,…}, and do not involve the operator Sn=Tn-PnT/En

The limit of N=(2,2) superconformal minimal models

The limit of families of two-dimensional conformal field theories has recently attracted attention in the context of AdS/CFT dualities. In our work we analyse the limit of N=(2,2) superconformal minimal models when the central charge approaches c=3. The limiting theory is a non-rational N=(2,2) superconformal theory, in which there is a continuum of chiral primary fields. We determine the spectrum of the theory, the three-point functions on the sphere, and the disc one-point functions.Comment: 37 pages, 3 figures; v2: minor corrections in section 5.3, version to be published in JHE

Argonne National Laboratory Reports

DISPL is a software package for solving some second-order nonlinear systems of partial differential equations including parabolic, elliptic, hyperbolic, and some mixed types such as parabolic-elliptic equations. Fairly general nonlinear boundary conditions are allowed as well as interface conditions for problems in an inhomogeneous media. The spatial domain is one- or two-dimensional with Cartesian, cylindrical, or spherical (in one dimension only) geometry. The numerical method is based on the use of Galerkin's procedure combined with the use of B-splines in order to reduce the system of PDE's to a system of ODE's. The latter system is then solved with a sophisticated ODE software package. Software features include extensive dump/restart facilities, free format input, moderate printed output capability, dynamic storage allocation, and three graphics packages

Driven motion of vortices in superconductors

The driven motion of vortices in the solid vortex state is analyzed with the time-dependent Ginzburg-Landau equations. In large-scale numerical simulations, carried out on the IBM Scalable POWERparallel (SP) system at Argonne National Laboratory, many hundreds of vortices are followed as they move under the influence of a Lorentz force induced by a transport current in the presence of a planar defect (similar to a twin boundary in YBa{sub 2}CU{sub 3}O{sub 7}). Correlations in the positions and velocities of the vortices in plastic and elastic motion are identified and compared. Two types of plastic motion are observed. Organized plastic motion displaying long-range orientational correlation and shorter-range velocity correlation occurs when the driving forces are small compared to the pinning forces in the twin boundary. Disorganized plastic motion displaying no significant correlation in either the velocities or orientation of the vortex system occurs when the driving and pinning forces axe of the same order

Time-dependent Ginzburg-Landau Simulations of vortex guidance by twin boundaries

The driven motion of vortices in the presence of a planar defect is simulated by means of the time-dependent Ginzburg-Landau equations. Guided motion of the vortices, both internal and external to the twin boundary, is found to occur over a range of driving forces. Experimental transport data on a single crystal of YBa{sub 2}Cu{sub 3}O{sub 7} are consistent with guided motion