Front tracking for hyperbolic systems

Glimm, James; Isaacson, Eli L.; Marchesin, D.; McBryan, Oliver A.

doi:10.1016/0196-8858(81)90040-3

Cited by 135 publications

(80 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…M has the definition the same problem in Ref. [ 11] with the front tracking method described there was depicted as having a stable front curve and no fingers. Table I •.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Methods to follow these time-dependent fronts in two space dimensions have been described by Richtmyer and Morton [17] and more recently by Noh and Woodward [15], Chorin [3J, Glimm, Isaacson, Marchesin and McBryan [11] and Hirt and Nichols [14]. The last reference contains a review of several front tracking techniques.…”

Section: Introductionmentioning

confidence: 99%

“…[17] and [11] the discontinuity curve is approximated by a number of points. The front is advanced in time by moving the points with the front speed, either in the direction normal to the front [17] or along the characteristics [11]. Another way of representing the front is suggested in Refs.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A front tracking method applied to Burgers' equation and two-phase porous flow

Lötstedt

1982

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…M has the definition the same problem in Ref. [ 11] with the front tracking method described there was depicted as having a stable front curve and no fingers. Table I •.…”

Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A front tracking method applied to Burgers' equation and two-phase porous flow

Lötstedt

1982

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…We are working to adapt FRONTIER, a front-tracking "hydrocode" developed at the State University of New York at Stony Brook (Glimm et al 1981(Glimm et al , 1985Grove 1989Grove , 1993, for application to solid explosive initiation problems. The principal elements required to treat such problems numerically are a continuum mechanics model (including appropriate treatment of boundary conditions) and a reacting mixture model.…”

Section: Introductionmentioning

confidence: 99%

Dynamics and Thermodynamics of Simple Two-Phase Reacting Mixtures for Application to Explosive Initiation Modeling

Starkenberg¹

2000

View full text Add to dashboard Cite

“…RT instability occurs when a fluid interface is accelerated in a direction opposite to the density gradient across the interface, while RM instability is induced by the refraction of shock waves through a fluid interface. FronTier is implemented for distributed memory parallel computers, and some of the fundamental algorithms used in this code are described in [23,8,30,34,22,31,18]. …”

mentioning

confidence: 99%

Interface Tracking for Axisymmetric Flows

Glimm¹,

Grove²,

Zhang³

2002

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

Abstract.A front tracking method for inviscid gas dynamics is presented. The key constructions and algorithms used in the code are described and the interrelations between shock capturing, interface dynamics, computational geometry, grid construction, and parallelism are discussed for the code as a whole. Validation is carried out by comparing the single mode bubble velocity for Rayleigh-Taylor instability with theoretical models and experimental results. The calculations are validated by mesh refinement studies and by the comparison of the asymptotic limit of the minimum radius r min → ∞ to a pure planar computation in two dimensions.Key words. front tracking, FronTier, interface, Rayleigh-Taylor AMS subject classifications. 76N15, 76T05, 76M20 PII. S1064827500366690 1. Introduction. Front tracking is an adaptive computational method in which a lower dimensional moving grid is fit to and follows distinguished waves in a flow. Tracked waves explicitly include jumps in the flow state across the waves and keep discontinuities sharp. A key feature is the avoidance of finite differencing across discontinuity fronts and thus the elimination of interfacial numerical diffusion including mass and vorticity diffusion. In addition, nonlinear instability and postshock oscillations are reduced at the tracked fronts. Front tracking as implemented in the code FronTier includes the ability to handle multidimensional wave interactions in both two [21,29,33] and three [20,19] space dimensions and is based on a composite algorithm that combines shock capturing on a spatial grid with a specialized treatment of the flow near the tracked fronts. Applications have included Rayleigh-Taylor (RT) [17,27,24,53,54] and Richtmyer-Meshkov (RM) [32,52,37,55,36] instability in two space dimensions and three dimensional planar RT instability [41,42,22,18]. RT instability occurs when a fluid interface is accelerated in a direction opposite to the density gradient across the interface, while RM instability is induced by the refraction of shock waves through a fluid interface. FronTier is implemented for distributed memory parallel computers, and some of the fundamental algorithms used in this code are described in [23,8,30,34,22,31,18].

show abstract

Front tracking for hyperbolic systems

Cited by 135 publications

References 5 publications

A front tracking method applied to Burgers' equation and two-phase porous flow

A front tracking method applied to Burgers' equation and two-phase porous flow

Dynamics and Thermodynamics of Simple Two-Phase Reacting Mixtures for Application to Explosive Initiation Modeling

Interface Tracking for Axisymmetric Flows

Contact Info

Product

Resources

About