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- Giacomo Dimarco, Lorenzo Pareschi
- SIAM J. Numerical Analysis
- 2011

We introduce a class of exponential Runge-Kutta integration methods for kinetic equations. The methods are based on a decomposition of the collision operator into an equilibrium and a non equilibrium part and are exact for relaxation operators of BGK type. For Boltzmann type kinetic equations they work uniformly for a wide range of relaxation times and… (More)

- Pierre Degond, Giacomo Dimarco, Luc Mieussens
- J. Comput. Physics
- 2007

This paper is a continuation of earlier work [6] in which we presented an automatic domain decomposition method for the solution of gas dynamics problems which require a localized resolution of the kinetic scale. The basic idea is to couple the macroscopic hydrodynamics model and the microscopic kinetic model through a buffer zone in which both equations… (More)

- Giacomo Dimarco, Lorenzo Pareschi
- Multiscale Modeling & Simulation
- 2008

- Pierre Degond, Giacomo Dimarco, Luc Mieussens
- J. Comput. Physics
- 2010

This paper collects the efforts done in our previous works [8],[11],[10] to build a robust multiscale kinetic-fluid solver. Our scope is to efficiently solve fluid dynamic problems which present non equilibrium localized regions that can move, merge, appear or disappear in time. The main ingredients of the present work are the followings ones: a fluid model… (More)

In this work we propose a new approach for the numerical simulation of kinetic equations through Monte Carlo schemes. We introduce a new technique which permits to reduce the variance of particle methods through a matching with a set of suitable macroscopic moment equations. In order to guarantee that the moment equations provide the correct solutions, they… (More)

- Giacomo Dimarco, Lorenzo Pareschi
- SIAM J. Scientific Computing
- 2010

In some recent works [11, 12] we developed a general framework for the construction of hybrid algorithms which are able to face efficiently the multiscale nature of some hyperbolic and kinetic problems. Here, at variance with respect to the previous methods, we construct a method form-fitting to any type of finite volume or finite difference scheme for the… (More)

- Russel E. Caflisch, Chiaming Wang, Giacomo Dimarco, Bruce I. Cohen, Andris M. Dimits
- Multiscale Modeling & Simulation
- 2008

If the collisional time scale for Coulomb collisions is comparable to the characteristic time scales for a plasma, then simulation of Coulomb collisions may be important for computation of kinetic plasma dynamics. This can be a computational bottleneck because of the large number of simulated particles and collisions (or phase-space resolution requirements… (More)

In this note we consider the development of a domain decomposition scheme directly obtained from the multiscale hybrid scheme described in [7]. The basic idea is to couple macroscopic and microscopic models in all cases in which the macroscopic model does not provide correct results. We will show that it's possible to view a Boltzmann-Euler domain… (More)

- Pierre Degond, Giacomo Dimarco
- J. Comput. Physics
- 2012

In the present work, we present a novel numerical algorithm to couple the Direct Simulation Monte Carlo method (DSMC) for the solution of the Boltzmann equation with a finite volume like method for the solution of the Euler equations. Recently we presented in [14],[16],[17] different methodologies which permit to solve fluid dynamics problems with localized… (More)

- Giacomo Dimarco, Lorenzo Pareschi
- SIAM J. Numerical Analysis
- 2013