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High-order Numerical Schemes for Kinetic Models with Applications in Plasma Physics


In the proposed research, we will devote to the mathematical and numerical analysis of kinetic models. Kinetic theory has wide applications in physical and social sciences, such as plasma physics, semi-conductors, polymers, traffic networking etc.

On the one hand, we want to propose and analyse systematic numerical methods for nonlinear kinetic models which have some challenging difficulties such as physical conservations, asymptotic regimes and stiffness. On the other hand, applications to plasma physics will be investigated, which are mainly high dimensional problems with multi-scale and complex geometries. Moreover collisions between particles for large time scale simulation need to be taken into account.
We would like to develop a class of less dissipative high order Hermite methods together with weighted essentially non-oscillatory (WENO) reconstructions to control spurious numerical oscillations, and high order asymptotic preserving (AP) discontinuous Galerkin (DG) schemes with implicit-explicit (IMEX) time discretizations for multi-scale stiff problems under unresolved meshes. More importantly, these developed numerical methods would satisfy the positivity preserving (PP) principle, such as positive density distribution functions for kinetic descriptions, which is often violated by high order numerical methods with physical meaningless values.

This project will combine the expertise of the Experienced Researcher Dr. Tao Xiong in high order PP flux limiters and high order AP DG-IMEX schemes, and the Host Dr. Francis Filbet in mathematical modellings and numerical tools for kinetic equations. The developed approaches will be translated to the study of turbulent plasma physics such as 4D drift kinetic, 5D gyro-kinetic and 6D kinetic models etc.

Field of science

  • /natural sciences/mathematics/applied mathematics/numerical analysis
  • /natural sciences/physical sciences/electromagnetism and electronics/electrical conductivity/semiconductor
  • /social sciences
  • /natural sciences/physical sciences/nuclear physics/nuclear fusion
  • /natural sciences/physical sciences/plasma physics
  • /natural sciences/mathematics/applied mathematics/mathematical model
  • /natural sciences/mathematics/pure mathematics/geometry

Call for proposal

See other projects for this call

Funding Scheme

MSCA-IF-EF-ST - Standard EF


Route De Narbonne 118
31062 Toulouse Cedex 9
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 185 076

Participants (1)


Participation ended

EU contribution
€ 0
Boulevard Du 11 Novembre 1918 Num43
69622 Villeurbanne Cedex
Activity type
Higher or Secondary Education Establishments