Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works

Boris, J. P.; Book, D. L.

doi:10.1016/0021-9991(73)90147-2

Cited by 1,971 publications

(891 citation statements)

References 8 publications

Supporting

Mentioning

848

Contrasting

Unclassified

Order By: Relevance

“…Another alternate is the flux-corrected transport algorithm of Boris & Book (1964), which is an Eulerian method based on Lagrangian considerations. Although this method can ensure positivity of the transported quantity and has been tested for several applications (Boris & Book, 1976), numerical diffusion necessitates the use of an anti-diffusion stage (Boris & Book, 1964), which must be tailored to the particular problem. However, if there is a sharp gradient in the solution, Eulerian numerical methods have difficulties (Woodward & Colella, 1984;LeVeque, 1990).…”

Section: Resultsmentioning

confidence: 99%

Energy-Conserving Simulation of Incompressible Electro-Osmotic and Pressure-Driven Flow

Alam

Bowman

2002

Theoretical and Computational Fluid Dynamics

View full text Add to dashboard Cite

Abstract.A numerical model for electro-osmotic flow is described. The advecting velocity field is computed by solving the incompressible Navier-Stokes equation. The method uses a semi-implicit multigrid algorithm to compute the divergence-free velocity at each grid point. The finite differences are second-order accurate and centered in space; however, the traditional second-order compact finite differencing of the Poisson equation for the pressure field is shown not to conserve energy in the inviscid limit. We have designed a non-compact finite differencing for the Laplacian in the pressure equation that allows exact energy conservation and affords second-order accuracy. The model also incorporates a new numerical method for passive scalar advection, called parcel advection, which accurately predicts the evolution of a passively traveling scalar pulse without requiring the addition of any artificial diffusion. The algorithm is used to confirm the experimentally observed asymmetric concentration profile that arises when an external pressure drop is imposed on electro-osmotic flow.

show abstract

Section: Resultsmentioning

confidence: 99%

Energy-Conserving Simulation of Incompressible Electro-Osmotic and Pressure-Driven Flow

Alam

Bowman

2002

Theoretical and Computational Fluid Dynamics

View full text Add to dashboard Cite

show abstract

“…To study the temporal evolution of velocity shear layers driven by the interaction of northern and southern coronal holes near solar minimum, we solved the inviscid MHD equations in spherical coordinates using a fourth-order fluxcorrected transport (FCT) algorithm [Boris and Book, 1973; Zalesak, 1979;DeVore, 1991]. FCT is designed to capture shocks and preserve discontinuities.…”

Section: Numerical Methods and Initial Conditionsmentioning

confidence: 99%

North‐south flows observed in the outer heliosphere at solar minimum: Vortex streets or corotating interaction regions?

Goldstein¹,

Roberts²,

Burlaga³

et al. 2001

J. Geophys. Res.

View full text Add to dashboard Cite

Abstract. During the last two solar minima in the distant heliosphere the equatorial heliospheric plasma velocity oscillated perpendicular to the ecliptic plane with an approximately 26-day period in the distant heliosphere. Two explanations have been proposed: compressive interactions between streams and velocity shear interactions that produce a Kfirmfin vortex street. The latter interpretation has been challenged on the basis that the velocity jumps are supersonic, thereby suppressing the Kelvin-Helmholtz (K-H) instability. Here we examine this issue using a time-dependent compressible magnetohydrodynamics code solved in spherical coordinates in the two-dimensional r -0 plane. We conclude that supersonic flow does suppress small-scale instabilities and that the classic Kfirmfin vortex street cannot be excited. Both velocity shear layers and stream interactions can, however, produce signatures in density, velocity, and magnetic field that resemble the observations. In particular, we find north-south variations of the flow velocity with a period that is approximately half that of the period of the variation in flow speed: a result insensitive to the thickness of the velocity shear layers. A depletion in density (and magnetic field magnitude) relative to the expected Parker value is predicted by the simulations that generate the north-south flow via velocity shear. The Voyager spacecraft observed a similar depletion in the outer heliosphere during the last two solar minima. When the effective tilt of the plasma sheet is increased, corotating interaction regions produce shock waves and other complex time-dependent evolution. We conclude that at solar minimum the observed north-south oscillations are a robust phenomenon that can form from either the interaction of fast and slow solar wind streams or from velocity shear. Which mechanism dominates is a consequence of the degree of tilt of the heliospheric current sheet, the magnitude of the velocity shear, and other physical parameters. However, the depletions seen in density and magnetic flux in the Voyager data suggest that velocity shear in the outer heliosphere at solar minimum may be the dominant cause of the observed north-south flow patterns.

show abstract

“…For details we refer to [26]. Let us note that the basic idea to negate dissipation by a corrector step was invented by Boris and Book [3,5]. However, the corrector step was realised technically quite differently in their original works.…”

Section: The Fct-schemementioning

confidence: 99%

Highly Accurate PDE-Based Morphology for General Structuring Elements

Breuß

Weickert

2009

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. Modelling the morphological processes of dilation and erosion with convex structuring elements with partial differential equations (PDEs) allows for digital scalability and subpixel accuracy. However, numerical schemes suffer from blur by dissipative artifacts. In our paper we present a family of so-called flux-corrected transport (FCT) schemes that addresses this problem for arbitrary convex structuring elements. The main characteristics of the FCT-schemes are: (i) They keep edges very sharp during the morphological evolution process, and (ii) they feature a high rotational invariance. Numerical experiments with diamonds and ellipses as structuring elements show that FCT-schemes are superior to standard schemes in the field of PDE-based morphology.

show abstract

Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works

Cited by 1,971 publications

References 8 publications

Energy-Conserving Simulation of Incompressible Electro-Osmotic and Pressure-Driven Flow

Energy-Conserving Simulation of Incompressible Electro-Osmotic and Pressure-Driven Flow

North‐south flows observed in the outer heliosphere at solar minimum: Vortex streets or corotating interaction regions?

Highly Accurate PDE-Based Morphology for General Structuring Elements

Contact Info

Product

Resources

About