# Asymptotic-Preserving scheme for a strongly anisotropic vorticity equation arising in fusion plasma modeling

@article{Mentrelli2018AsymptoticPreservingSF, title={Asymptotic-Preserving scheme for a strongly anisotropic vorticity equation arising in fusion plasma modeling}, author={A. Mentrelli and C. Negulescu}, journal={Comput. Phys. Commun.}, year={2018}, volume={229}, pages={116-128} }

Abstract The electric potential is an essential quantity for the confinement process of tokamak plasmas, with important impact on the performances of fusion reactors. Understanding its evolution in the peripheral region – the part of the plasma interacting with the wall of the device – is of crucial importance, since it governs the boundary conditions for the burning core plasma. The aim of the present paper is to study numerically the evolution of the electric potential in this peripheral… Expand

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#### References

SHOWING 1-10 OF 26 REFERENCES

Existence and uniqueness of the electric potential profile in the edge of tokamak plasmas when constrained by the plasma-wall boundary physics

- Physics
- 2008

The electric potential plays a key role in the
confinement properties of tokamak plasmas, with the subsequent
impact on the performances of fusion reactors. Understanding its
structure in the… Expand

Asymptotic-preserving scheme for highly anisotropic non-linear diffusion equations

- Mathematics, Computer Science
- J. Comput. Phys.
- 2012

The authors propose a numerical scheme based on an asymptotic-preserving (AP) reformulation of this non-linear evolution problem, generalizing the ideas introduced in a previous paper for the case of elliptic anisotropic problems and it is shown that the scheme is capable to deal with problems characterized by a high degree of anisotropy, thus proving to be suitable for the study of an isotropic diffusion in magnetically confined plasmas. Expand

Highly anisotropic temperature balance equation and its asymptotic-preserving resolution

- Physics, Mathematics
- 2012

This paper deals with the numerical study of a nonlinear, strongly anisotropic heat equation. The use of standard schemes in this situation leads to poor results, due to the high anisotropy. An… Expand

Highly anisotropic nonlinear temperature balance equation and its numerical solution using asymptotic-preserving schemes of second order in time

- Mathematics
- 2014

This paper deals with the numerical study of a nonlinear, strongly anisotropic heat equation. The use of standard schemes in this situation leads to poor results, due to the high anisotropy. An… Expand

An asymptotic preserving scheme based on a micro-macro decomposition for collisional Vlasov equations: diffusion and high-field scaling limits.

- Mathematics
- 2011

In this work, we extend the micro-macro decomposition based numerical schemes developed in [3]
to the collisional Vlasov-Poisson model in the diffusion and high-field asymptotics. In doing so, we… Expand

Asymptotic-Preserving Schemes for Fluid Models of Plasmas

- Physics, Mathematics
- 2011

These notes summarize a series of works related to the numerical approximation of plasma fluid problems. We construct so-called 'Asymptotic-Preserving' schemes which are valid for a large range of… Expand

An asymptotic-preserving method for highly anisotropic elliptic equations based on a Micro-Macro decomposition

- Mathematics, Computer Science
- J. Comput. Phys.
- 2012

A very efficient asymptotic preserving scheme for the resolution of highly anisotropic diffusion equations with uniform convergence with respect to the anisotropy parameter 0<e?1 and its considerable advantages are pointed out. Expand

The TOKAM3X code for edge turbulence fluid simulations of tokamak plasmas in versatile magnetic geometries

- Physics, Computer Science
- J. Comput. Phys.
- 2016

The new code TOKAM3X simulates plasma turbulence in full torus geometry including the open field lines of the Scrape-off Layer (SOL) and the edge closed field lines region in the vicinity of the… Expand

A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit

- Mathematics, Computer Science
- SIAM J. Sci. Comput.
- 2008

A new numerical scheme for linear transport equations based on a decomposition of the distribution function into equilibrium and nonequilibrium parts that is asymptotic preserving in the following sense: when the mean free path of the particles is small. Expand

A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources

- Mathematics, Computer Science
- J. Comput. Phys.
- 2010

A general time-discrete framework to design asymptotic-preserving schemes for initial value problem of the Boltzmann kinetic and related equations, which can capture the macroscopic fluid dynamic (Euler) limit even if the small scale determined by the Knudsen number is not numerically resolved. Expand