A moving interface method for dynamic kinetic–fluid coupling

Degond, Pierre; Dimarco, Giacomo; Mieussens, Luc

doi:10.1016/j.jcp.2007.08.027

Cited by 36 publications

(90 citation statements)

References 22 publications

(41 reference statements)

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“…We have shown a concise analysis for a simple, but relevant, model problem which showed that this type of coupling leads to a very efficient heterogeneous domain decomposition method. This method can be viewed as a formalisation of a coupling technique for very complex problems, see for example [5,6] for the coupling between kinetic and hydrodynamic equations. In such a coupling, the partition between the different fuzzy domains can evolve with time and can even adapt automatically to the local conditions using some local criterion, see [6].…”

Section: Resultsmentioning

confidence: 99%

“…This assumption has been used at least in two different series of papers: the first one is in physics for the approximation of neutrino radiative transfer in core-collapse supernovae [11,2,3], and the second one is in mathematics for the coupling between the kinetic equation and approximations of it (diffusion, Euler, Navier-Stokes...) [8,5,6,7].…”

Section: Motivationmentioning

confidence: 99%

“…The methods of Degond et al [8,5,6,7] belong to the eFDDM class, but the IDSA [11,2,3] is an example of an iFDDM.…”

Section: Remarkmentioning

confidence: 99%

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Fuzzy Domain Decomposition: A New Perspective on Heterogeneous DD Methods

Gander

Michaud

2014

Lecture Notes in Computational Science and Engineering

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In a wide variety of physical problems, the complexity of the physics involved is such that it is necessary to develop approximations, because the complete physical model is simply too costly. Sometimes however the complete model is essential to capture all the physics, and often this is only in part of the domain of interest. One can then use heterogeneous domain decomposition techniques: if we know a priori where an approximation is valid, we can divide the computational domain into subdomains in which a particular approximation is valid and the topic of heterogeneous domain decomposition methods is to find the corresponding coupling conditions to insure that the overall coupled solution is a good approximation of the solution of the complete physical model. For an overview of such techniques, see [9,10] and references therein. However, there are many physical problems where it is not a priori known where which approximation is valid. In such problems, one needs to track the domain of validity of a particular approximation, and this is usually not an easy task. An example of such a method is the -method, see [4,1].In this contribution, we introduce a new formalism for heterogeneous domain decomposition, which is not based on a sharp decomposition into subdomains where different models are valid. The main idea relies on the notion of Fuzzy Sets introduced by Zadeh [12] in 1965. The Fuzzy Set Theory relaxes the notion of belonging to a set through membership functions to (fuzzy) sets that account for partially belonging to a set. In the context of heterogeneous domain decomposition, this could be useful if one assumes that the computational domain can be decomposed into fuzzy sets that form a partition of the domain in a sense that needs to be specified. Once such a partition is given, one can compute the solution of the coupled problem using the membership functions. Note that the membership functions can depend on space and time and therefore can take into account a change in the validity domain of a particular approximation. We show here that this technique leads to an excellent coupling strategy for the 1D advection dominated diffusion problem. Such a domain decomposition method would be able, in principle, to take into account part of the domain where none of the available approximations are valid under the assumption that a combination of them is a good enough approximation there.On the assumption u = u 1

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Section: Resultsmentioning

confidence: 99%

Section: Motivationmentioning

confidence: 99%

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Fuzzy Domain Decomposition: A New Perspective on Heterogeneous DD Methods

Gander

Michaud

2014

Lecture Notes in Computational Science and Engineering

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“…Note also that the initial data is automatically switched thanks to the indicator function, as described in §4.2.1. See also [12]. We also recall that f n E,i,…”

Section: Relaxation Step In Es-bgk Cellsmentioning

confidence: 93%

“…Beside the difficulty in the design of effective breakdown criteria, see also the discussion in [20] and [12], another difficulty in domain decomposition algorithms is due to the need of exchanging information between the stochastic solution obtained with DSMC and the deterministic solution of the continuum solver. This can be circumvented reducing noise through averaging, as in [17], where the stochastic solution is computed with a smaller grid in space and time with respect to the macroscopic solution, and thus it is averaged over the larger macroscopic cells.…”

Section: Introductionmentioning

confidence: 99%

A hybrid method for hydrodynamic-kinetic flow – Part II – Coupling of hydrodynamic and kinetic models

Alaia

Puppo

2012

Journal of Computational Physics

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In this work we present a non stationary domain decomposition algorithm for multiscale hydrodynamic-kinetic problems, in which the Knudsen number may span from equilibrium to highly rarefied regimes. Our approach is characterized by using the full Boltzmann equation for the kinetic regime, the Compressible Euler equations for equilibrium, with a buffer zone in which the BGK-ES equation is used to represent the transition between fully kinetic to equilibrium flows.In this fashion, the Boltzmann solver is used only when the collision integral is non-stiff, and the mean free path is of the same order as the mesh size needed to capture variations in macroscopic quantities. Thus, in principle, the same mesh size and time steps can be used in the whole computation. Moreover, the time step is limited only by convective terms.Since the Boltzmann solver is applied only in wholly kinetic regimes, we use the reduced noise DSMC scheme we have proposed in Part I of the present work. This ensures a smooth exchange of information across the different domains, with a natural way to construct interface numerical fluxes. Several tests comparing our hybrid scheme with full Boltzmann DSMC computations show the good agreement between the two solutions, on a wide range of Knudsen numbers.

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Godlewski¹,

Raviart²

2020

Applied Mathematical Sciences

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A moving interface method for dynamic kinetic–fluid coupling

Cited by 36 publications

References 22 publications

Fuzzy Domain Decomposition: A New Perspective on Heterogeneous DD Methods

Fuzzy Domain Decomposition: A New Perspective on Heterogeneous DD Methods

A hybrid method for hydrodynamic-kinetic flow – Part II – Coupling of hydrodynamic and kinetic models

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