14,633 research outputs found
A class of residual distribution schemes and their relation to relaxation systems
Residual distributions (RD) schemes are a class of of high-resolution finite
volume methods for unstructured grids. A key feature of these schemes is that
they make use of genuinely multidimensional (approximate) Riemann solvers as
opposed to the piecemeal 1D Riemann solvers usually employed by finite volume
methods. In 1D, LeVeque and Pelanti [J. Comp. Phys. 172, 572 (2001)] showed
that many of the standard approximate Riemann solver methods (e.g., the Roe
solver, HLL, Lax-Friedrichs) can be obtained from applying an exact Riemann
solver to relaxation systems of the type introduced by Jin and Xin [Comm. Pure
Appl. Math. 48, 235 (1995)]. In this work we extend LeVeque and Pelanti's
results and obtain a multidimensional relaxation system from which
multidimensional approximate Riemann solvers can be obtained. In particular, we
show that with one choice of parameters the relaxation system yields the
standard N-scheme. With another choice, the relaxation system yields a new
Riemann solver, which can be viewed as a genuinely multidimensional extension
of the local Lax-Friedrichs scheme. This new Riemann solver does not require
the use Roe-Struijs-Deconinck averages, nor does it require the inversion of an
m-by-m matrix in each computational grid cell, where is the number of
conserved variables. Once this new scheme is established, we apply it on a few
standard cases for the 2D compressible Euler equations of gas dynamics. We show
that through the use of linear-preserving limiters, the new approach produces
numerical solutions that are comparable in accuracy to the N-scheme, despite
being computationally less expensive.Comment: 46 pages, 14 figure
Real-time evolution for weak interaction quenches in quantum systems
Motivated by recent experiments in ultracold atomic gases that explore the
nonequilibrium dynamics of interacting quantum many-body systems, we
investigate the nonequilibrium properties of a Fermi liquid. We apply an
interaction quench within the Fermi liquid phase of the Hubbard model by
switching on a weak interaction suddenly; then we follow the real-time dynamics
of the momentum distribution by a systematic expansion in the interaction
strength based on the flow equation method. In this paper we derive our main
results, namely the applicability of a quasiparticle description, the
observation of a new type of quasi-stationary nonequilibrium Fermi liquid like
state and a delayed thermalization of the momentum distribution. We explain the
physical origin of the delayed relaxation as a consequence of phase space
constraints in fermionic many-body systems. This brings about a close relation
to similar behavior of one-particle systems which we illustrate by a discussion
of the squeezed oscillator; we generalize to an extended class of systems with
discrete energy spectra and point out the generic character of the
nonequilibrium Fermi liquid results for weak interaction quenches. Both for
discrete and continuous systems we observe that particular nonequilibrium
expectation values are twice as large as their corresponding analogues in
equilibrium. For a Fermi liquid, this shows up as an increased
correlation-induced reduction of the quasiparticle residue in nonequilibrium.Comment: 54 page
Spectral methods for modeling supersonic chemically reacting flow fields
A numerical algorithm was developed for solving the equations describing chemically reacting supersonic flows. The algorithm employs a two-stage Runge-Kutta method for integrating the equations in time and a Chebyshev spectral method for integrating the equations in space. The accuracy and efficiency of the technique were assessed by comparison with an existing implicit finite-difference procedure for modeling chemically reacting flows. The comparison showed that the procedure presented yields equivalent accuracy on much coarser grids as compared to the finite-difference procedure with resultant significant gains in computational efficiency
Concurrent Multiscale Computing of Deformation Microstructure by Relaxation and Local Enrichment with Application to Single-Crystal Plasticity
This paper is concerned with the effective modeling of deformation microstructures within a concurrent multiscale computing framework. We present a rigorous formulation of concurrent multiscale computing based on relaxation; we establish the connection between concurrent multiscale computing and enhanced-strain elements; and we illustrate the approach in an important area of application, namely, single-crystal plasticity, for which the explicit relaxation of the problem is derived analytically. This example demonstrates the vast effect of microstructure formation on the macroscopic behavior of the sample, e.g., on the force/travel curve of a rigid indentor. Thus, whereas the unrelaxed model results in an overly stiff response, the relaxed model exhibits a proper limit load, as expected. Our numerical examples additionally illustrate that ad hoc element enhancements, e.g., based on polynomial, trigonometric, or similar representations, are unlikely to result in any significant relaxation in general
- …