A conservative finite element method for one-dimensional stefan problems with appearing and disappearing phases

Bonnerot, R; Jamet, Pierre

doi:10.1016/0021-9991(81)90101-7

Cited by 37 publications

(18 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…He proved optimal order convergence results under a mild constraint on the number of discontinuous changes in the function spaces. Jamet's work with R. Bonnerot on the Stefan problem [4], [5], [6] presents a chain of ideas that has culminated in a method that has a continuously moving mesh that tracks the fronts in a multiphase Stefan problem; their method also admits discontinuous mesh changes. They used a related approach in [7] for compressible flow calculations, and Jamet has analyzed a one-dimensional parabolic analog in [13].…”

mentioning

confidence: 99%

“…Let, for all sufficiently regular maps xp of [0, T] into //'(fi), (5)(6)(7)(8) [ Miller has defined a class of methods for systematically moving the mesh associated with a finite element function space. These procedures, which he calls MFE's or moving finite element methods, seem experimentally to be quite effective for problems with sharp fronts [17], [18], [11], [2].…”

mentioning

confidence: 99%

See 1 more Smart Citation

Mesh Modification for Evolution Equations

Dupont¹

1982

Mathematics of Computation

View full text Add to dashboard Cite

Abstract. Finite element methods for which the underlying function spaces change with time are studied. The error estimates produced are all in norms that are very naturally associated with the problems. In some cases the Galerkin solution error can be seen to be quasi-optimal. K. Miller's moving finite element method is studied in one space dimension; convergence is proved for the case of smooth solutions of parabolic problems. Most, but not all, of the analysis is done on linear problems. Although second order parabolic equations are emphasized, there is also some work on first order hyperbolic and Sobolev equations.

show abstract

mentioning

confidence: 99%

mentioning

confidence: 99%

Mesh Modification for Evolution Equations

Dupont¹

1982

Mathematics of Computation

View full text Add to dashboard Cite

show abstract

“…Bonnerot and Jamet [3] extended the adaptive space-time finite element scheme reported in [4] to deal with multi-phase problems. They used curved triangular elements for appearing boundaries and curved trapezoidal elements elsewhere.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper a boundary element based technique, capable of dealing with multi-moving boundaries with great ease, is presented and tested on a heat transfer problem involving appearing and disappearing phases with several simultaneous moving boundaries. For comparison purposes the collapse of a solid wall treated in references [2,3] is also considered.…”

Section: Introductionmentioning

confidence: 99%

A Boundary Element Method for Multiple Moving Boundary Problems

Zerroukat

Wrobel

1997

Journal of Computational Physics

View full text Add to dashboard Cite

“…There are four methods to deal with phase appearance and disappearance problems: (1) conventional models with switches to be used in grid cells where conversion of single-phase to two-phase or vice versa occurs (Bonnerot and Jamet 1981;Pruess 2004;Zhu et al 2004;Chen et al 2006;Bruining and Marchesin 2007); (2) a non-equilibrium source term in all the equations is used that drives the system toward equilibrium (Ben-Omran and Green 1978;Bruining and Van Duijn 2006); (3) compositional-space-parameterization approach (Voskov and Tchelepi 2009;Voskov 2010), which can be thought of as an extension of the conventional approach; and (4) the negative saturation method (Abadpour and Panfilov 2009;Panfilov and Rasoulzadeh 2010) that avoids the use of switches and separate equations.…”

Section: Introductionmentioning

confidence: 99%

Negative Saturation Approach for Non-Isothermal Compositional Two-Phase Flow Simulations

2011

View full text Add to dashboard Cite

This article deals with developing a solution approach, called the non-isothermal negative saturation (NegSat) solution approach. The NegSat solution approach solves efficiently any non-isothermal compositional flow problem that involves phase disappearance, phase appearance, and phase transition. The advantage of the solution approach is that it circumvents using different equations for single-phase and two-phase regions and the ensuing unstable procedure. This paper shows that the NegSat solution approach can also be used for non-isothermal systems. The NegSat solution approach can be implemented efficiently in numerical simulators to tackle modeling issues for mixed CO 2 -water injection in geothermal reservoirs, thermal recovery processes, and for multicontact miscible and immiscible gas injection in oil reservoirs. We illustrate the approach by way of example to cold mixed CO 2 -water injection in a 1D geothermal reservoir. The solution is compared with an analytical solution obtained with the wave-curve method (method of characteristics) and shows excellent agreement. A complete set of simulations is carried out, which identifies six bifurcations. The two main bifurcations are (1) when the most downstream compositional wave is replaced by a compositional shock and (2) when an extra Buckley-Leverett rarefaction appears. The plot of the useful energy (exergy) versus the CO 2 storage capacity shows a Z -shape. The top horizontal part represents a branch of high exergy recovery/relatively lower storage capacity, whereas the bottom part represents a branch of lower exergy recovery/higher storage capacity.

show abstract

A conservative finite element method for one-dimensional stefan problems with appearing and disappearing phases

Cited by 37 publications

References 9 publications

Mesh Modification for Evolution Equations

Mesh Modification for Evolution Equations

A Boundary Element Method for Multiple Moving Boundary Problems

Negative Saturation Approach for Non-Isothermal Compositional Two-Phase Flow Simulations

Contact Info

Product

Resources

About