Augmented versions of the HLL and HLLC Riemann solvers including source terms in one and two dimensions for shallow flow applications

AbstractSeveral important PDE systems, like magnetohydrodynamics and computational electrodynamics, are known to support involutions where the divergence of a vector field evolves in divergence-free or divergence constraint-preserving fashion. Recently, new classes of PDE systems have emerged for hyperelasticity, compressible multiphase flows, so-called first-order reductions of the Einstein field equations, or a novel first-order hyperbolic reformulation of Schrödinger’s equation, to name a few, where the involution in the PDE supports curl-free or curl constraint-preserving evolution of a vector field. We study the problem of curl constraint-preserving reconstruction as it pertains to the design of mimetic finite volume (FV) WENO-like schemes for PDEs that support a curl-preserving involution. (Some insights into discontinuous Galerkin (DG) schemes are also drawn, though that is not the prime focus of this paper.) This is done for two- and three-dimensional structured mesh problems where we deliver closed form expressions for the reconstruction. The importance of multidimensional Riemann solvers in facilitating the design of such schemes is also documented. In two dimensions, a von Neumann analysis of structure-preserving WENO-like schemes that mimetically satisfy the curl constraints, is also presented. It shows the tremendous value of higher order WENO-like schemes in minimizing dissipation and dispersion for this class of problems. Numerical results are also presented to show that the edge-centered curl-preserving (ECCP) schemes meet their design accuracy. This paper is the first paper that invents non-linearly hybridized curl-preserving reconstruction and integrates it with higher order Godunov philosophy. By its very design, this paper is, therefore, intended to be forward-looking and to set the stage for future work on curl involution-constrained PDEs.

Download Full-text

A Generalized Relaxation Method for Transport and Diffusion of Pollutant Models in Shallow Water

Computational Methods in Applied Mathematics ◽

10.2478/cmam-2004-0023 ◽

2004 ◽

Vol 4 (4) ◽

pp. 410-430 ◽

Cited By ~ 9

Author(s):

A.I. Delis ◽

Th. Katsaounis

Keyword(s):

Transport Equation ◽

Shallow Water ◽

Relaxation Method ◽

Two Dimensions ◽

Special Treatment ◽

Test Problems ◽

Riemann Solvers ◽

Relaxation Scheme ◽

Transport And Diffusion ◽

And Diffusion

AbstractWe present a numerical method based on finite difference relaxation approximations for computing the transport and diffusion of a passive pollutant by a water flow. The flow is modeled by the well-known shallow water equations and the pollutant propagation is described by a transport equation. The previously developed nonoscillatory relaxation scheme is generalized to cover problems with pollutant trans- port, in one and two dimensions and source terms, resulting in a class of methods of the first and the second order of accuracy in space and time. The methods are based on the classical relaxation models combined with a Runge-Kutta time splitting scheme, where neither Riemann solvers nor characteristic decompositions are needed. Numerical results are presented for several benchmark test problems. The schemes presented are verified by comparing the results with documented ones, proving that no special treatment is needed for the transport equation in order to obtain accurate results.

Download Full-text

Improved Riemann solvers for complex transport in two-dimensional unsteady shallow flow

Journal of Computational Physics ◽

10.1016/j.jcp.2011.05.022 ◽

2011 ◽

Vol 230 (19) ◽

pp. 7202-7239 ◽

Cited By ~ 13

Author(s):

J. Murillo ◽

P. García-Navarro

Keyword(s):

Two Dimensional ◽

Shallow Flow ◽

Riemann Solvers

Download Full-text

The tangled web of agency

Behavioral and Brain Sciences ◽

10.1017/s0140525x17001170 ◽

2018 ◽

Vol 41 ◽

Author(s):

Alain Pe-Curto ◽

Julien A. Deonna ◽

David Sander

Keyword(s):

Two Dimensions ◽

Bad Company

AbstractWe characterize Doris's anti-reflectivist, collaborativist, valuational theory along two dimensions. The first dimension is socialentanglement, according to which cognition, agency, and selves are socially embedded. The second dimension isdisentanglement, the valuational element of the theory that licenses the anchoring of agency and responsibility in distinct actors. We then present an issue for the account: theproblem of bad company.

Download Full-text

A transmission electron microscopic study of structural transitions in fast ionic conductors

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100125713 ◽

1987 ◽

Vol 45 ◽

pp. 156-157

Author(s):

R. B. Queenan ◽

P. K. Davies

Keyword(s):

Optical Properties ◽

Ionic Conduction ◽

Recent Observation ◽

Ionic Conductivities ◽

Sodium Aluminate ◽

Two Dimensions ◽

Ionic Conductors ◽

Electron Microscopic ◽

Transmission Electron ◽

Trivalent Cations

Na ß“-alumina (Na1.67Mg67Al10.33O17) is a non-stoichiometric sodium aluminate which exhibits fast ionic conduction of the Na+ ions in two dimensions. The Na+ ions can be exchanged with a variety of mono-, di-, and trivalent cations. The resulting exchanged materials also show high ionic conductivities.Considerable interest in the Na+-Nd3+-ß“-aluminas has been generated as a result of the recent observation of lasing in the pulsed and cw modes. A recent TEM investigation on a 100% exchanged Nd ß“-alumina sample found evidence for the intergrowth of two different structure types. Microdiffraction revealed an ordered phase coexisting with an apparently disordered phase, in which the cations are completely randomized in two dimensions. If an order-disorder transition is present then the cooling rates would be expected to affect the microstructures of these materials which may in turn affect the optical properties. The purpose of this work was to investigate the affect of thermal treatments upon the micro-structural and optical properties of these materials.

Download Full-text

Laser Scanning Confocal Microscopy and Three-Dimesnsional Reconstruction of the Mitotic Spindles of Unequally Dividing Embryonic Cells

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100158376 ◽

1990 ◽

Vol 48 (3) ◽

pp. 166-167

Author(s):

J. Holy ◽

G. Schatten

Keyword(s):

Confocal Microscopy ◽

Mitotic Spindle ◽

Laser Scanning ◽

Three Dimensional ◽

Laser Scanning Confocal Microscopy ◽

Two Dimensions ◽

Embryonic Cells ◽

Mitotic Spindles ◽

Cleavage Division ◽

Scanning Confocal Microscopy

One of the classic limitations of light microscopy has been the fact that three dimensional biological events could only be visualized in two dimensions. Recently, this shortcoming has been overcome by combining the technologies of laser scanning confocal microscopy (LSCM) and computer processing of microscopical data by volume rendering methods. We have employed these techniques to examine morphogenetic events characterizing early development of sea urchin embryos. Specifically, the fourth cleavage division was examined because it is at this point that the first morphological signs of cell differentiation appear, manifested in the production of macromeres and micromeres by unequally dividing vegetal blastomeres.The mitotic spindle within vegetal blastomeres undergoing unequal cleavage are highly polarized and develop specialized, flattened asters toward the micromere pole. In order to reconstruct the three-dimensional features of these spindles, both isolated spindles and intact, extracted embryos were fluorescently labeled with antibodies directed against either centrosomes or tubulin.

Download Full-text

Instrumental and Ideological Union Commitment: Longitudinal Assessment of Construct Validity

European Journal of Psychological Assessment ◽

10.1027//1015-5759.17.2.98 ◽

2001 ◽

Vol 17 (2) ◽

pp. 98-111 ◽

Cited By ~ 1

Author(s):

Anders Sjöberg ◽

Magnus Sverke

Keyword(s):

Construct Validity ◽

Temporal Stability ◽

Strong Support ◽

Internal Consistency Reliability ◽

Measurement Model ◽

Two Dimensions ◽

Model Parameters ◽

Longitudinal Assessment ◽

Union Commitment ◽

Union Participation

Summary: Previous research has identified instrumentality and ideology as important aspects of member attachment to labor unions. The present study evaluated the construct validity of a scale designed to reflect the two dimensions of instrumental and ideological union commitment using a sample of 1170 Swedish blue-collar union members. Longitudinal data were used to test seven propositions referring to the dimensionality, internal consistency reliability, and temporal stability of the scale as well as postulated group differences in union participation to which the scale should be sensitive. Support for the hypothesized factor structure of the scale and for adequate reliabilities of the dimensions was obtained and was also replicated 18 months later. Tests for equality of measurement model parameters and test-retest correlations indicated support for the temporal stability of the scale. In addition, the results were consistent with most of the predicted differences between groups characterized by different patterns of change/stability in union participation status. The study provides strong support for the construct validity of the scale and indicates that it can be used in future theory testing on instrumental and ideological union commitment.

Download Full-text

The Prediction of Problem-Solving Assessed Via Microworlds

European Journal of Psychological Assessment ◽

10.1027/1015-5759/a000263 ◽

2016 ◽

Vol 32 (4) ◽

pp. 298-306 ◽

Cited By ~ 7

Author(s):

Samuel Greiff ◽

Katarina Krkovic ◽

Jarkko Hautamäki

Keyword(s):

Working Memory ◽

Problem Solving ◽

Complex Problem ◽

Two Dimensions ◽

Assessment Instruments ◽

Complex Problem Solving ◽

Visual Spatial ◽

Rule Knowledge ◽

Rule Application ◽

Fluid Reasoning

Abstract. In this study, we explored the network of relations between fluid reasoning, working memory, and the two dimensions of complex problem solving, rule knowledge and rule application. In doing so, we replicated the recent study by Bühner, Kröner, and Ziegler (2008) and the structural relations investigated therein [ Bühner, Kröner, & Ziegler, (2008) . Working memory, visual-spatial intelligence and their relationship to problem-solving. Intelligence, 36, 672–680]. However, in the present study, we used different assessment instruments by employing assessments of figural, numerical, and verbal fluid reasoning, an assessment of numerical working memory, and a complex problem solving assessment using the MicroDYN approach. In a sample of N = 2,029 Finnish sixth-grade students of which 328 students took the numerical working memory assessment, the findings diverged substantially from the results reported by Bühner et al. Importantly, in the present study, fluid reasoning was the main source of variation for rule knowledge and rule application, and working memory contributed only a little added value. Albeit generally in line with previously conducted research on the relation between complex problem solving and other cognitive abilities, these findings directly contrast the results of Bühner et al. (2008) who reported that only working memory was a source of variation in complex problem solving, whereas fluid reasoning was not. Explanations for the different patterns of results are sought, and implications for the use of assessment instruments and for research on interindividual differences in complex problem solving are discussed.

Download Full-text