The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques

Merkle, C.; Rohde, Christian

doi:10.1051/m2an:2007048

Cited by 39 publications

(47 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is the case, for instance, of models describing the dynamics of liquid-vapor phase transitions in compressible fluids, or of solid-solid phase transformations in materials such as memory alloys. For numerical work in this direction we refer to [18,19,10,31,32].…”

Section: State Of the Artmentioning

confidence: 99%

“…In [19], Hou, LeFloch, and Zhong proposed a class of converging schemes for the computation of propagating solid-solid phase boundaries and, more recently, Merckle and Rohde [32] developed a ghost-fluid type algorithm for a model of dynamics of phase transition. Those schemes provide satisfactory numerical results, as nonclassical discontinuities are sharply and accurately computed.…”

Section: Objectives Of This Papermentioning

confidence: 99%

See 1 more Smart Citation

Convergent and conservative schemes for nonclassical solutions based on kinetic relations. I

Boutin¹,

Chalons²,

Lagoutìère³

et al. 2008

Interfaces Free Bound.

View full text Add to dashboard Cite

We propose a new numerical approach to computing nonclassical solutions to hyperbolic conservation laws. The class of finite difference schemes presented here is fully conservative and keeps nonclassical shock waves as sharp interfaces, unlike standard finite difference schemes. The main challenge is to achieve, at the discretization level, a consistency property with respect to a prescribed kinetic relation. The latter is required for the selection of physically meaningful nonclassical shocks. Our method is based on a reconstruction technique performed in each computational cell that may contain a nonclassical shock. To validate this approach, we establish several consistency and stability properties, and we perform careful numerical experiments. The convergence of the algorithm toward the physically meaningful solutions selected by a kinetic relation is demonstrated numerically for several test cases, including concave-convex as well as convex-concave flux functions.

show abstract

Section: State Of the Artmentioning

confidence: 99%

Section: Objectives Of This Papermentioning

confidence: 99%

Convergent and conservative schemes for nonclassical solutions based on kinetic relations. I

Boutin¹,

Chalons²,

Lagoutìère³

et al. 2008

Interfaces Free Bound.

View full text Add to dashboard Cite

show abstract

“…This method of calculating two different fluxes for each phase results in a solution where variables such as the density remain discontinuous across the (computational) interface and the typical numerical smearing of discontinuities in numerical schemes is avoided. For piecewise constant approximations the method is similar to the ghostfluid method [7,16], where two different fluxes are obtained via additional ghost states near the interface.…”

Section: Numerical Fluxes At the Computational Interfacementioning

confidence: 99%

“…The effect of the trace conditions (6) and in particular the Young-Laplace equation (7) enters via a kind of micro-scale model 1 which will be a generalized Riemann problem with non-homogeneous jump conditions. For the curvature-free case and using a completely different mass transfer via the interface this approach has been introduced in [5,11,16]. It relies on ghostfluid ideas tracing back to [7].…”

Section: Introductionmentioning

confidence: 99%

A multiscale method for compressible liquid-vapor flow with surface tension

2012

Self Cite

View full text Add to dashboard Cite

Abstract. Discontinuous Galerkin methods have become a powerful tool for approximating the solution of compressible flow problems. Their direct use for two-phase flow problems with phase transformation is not straightforward because this type of flows requires a detailed tracking of the phase front. We consider the fronts in this contribution as sharp interfaces and propose a novel multiscale approach. It combines an efficient high-order Discontinuous Galerkin solver for the computation in the bulk phases on the macro-scale with the use of a generalized Riemann solver on the micro-scale. The Riemann solver takes into account the effects of moderate surface tension via the curvature of the sharp interface as well as phase transformation. First numerical experiments in three space dimensions underline the overall performance of the method.

show abstract

“…The first of such schemes is the Glimm-type ansatz in [18], see also [5]. Deterministic versions that use an extra tracking of the undercompressive waves have been introduced in [4,14,23,24,30]. The drawback of all these schemes is the fact that the discrete solution does not conserve the integral of the solution.…”

Section: Introduction Let F ∈ Cmentioning

confidence: 99%

A Conservative and Convergent Scheme for Undercompressive Shock Waves

Chalons¹,

Engel²,

Rohde³

2014

SIAM J. Numer. Anal.

View full text Add to dashboard Cite

Abstract. Undercompressive shock waves arise in numerous physical applications. We propose a class of conservative finite-volume type schemes to approximate weak solutions of conservation laws that contain undercompressive shock waves. We prove the convergence of a subsequence of approximate solutions towards a generalized entropy solution if the mesh width tends to zero. The proof relies on a refined BV compactness analysis, which accounts for the effect of the kinetic relation that drives the undercompressive wave. At the same time we establish a new proof for the existence of solutions to the underlying model. Numerical experiments supplement the analytical results.

show abstract

The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques

Cited by 39 publications

References 39 publications

Convergent and conservative schemes for nonclassical solutions based on kinetic relations. I

Convergent and conservative schemes for nonclassical solutions based on kinetic relations. I

A multiscale method for compressible liquid-vapor flow with surface tension

A Conservative and Convergent Scheme for Undercompressive Shock Waves

Contact Info

Product

Resources

About