MESH-FREE FORMULATION OF TWO DIMENSIONAL DARWIN MODEL

In many astrophysical and fusion applications the CFL stability condition implies strong computational efforts. We propose here a magneto-inductive (Darwin) plasma model, which neglects retardation effects so that the electromagnetic propagation speed is effectively infinite. In this way long timescale phenomena can be investigated without the need to explicitly resolve wave propagation. By neglecting the solenoidal part of the displacement current in Ampere’s law and setting up the vector potential as a divergence-free field, the Maxwell- Darwin equations are converted from hyperbolic to elliptic partial differential equations, which can then be solved with the help of tree methods. Our purpose is to formulate a mesh-free model based on particles with finite-size shape function to avoid singularities in pair potential. The main challenge of this work is to construct a robust method which avoids the numerical instabilities due to combination of Darwin approximation with standard integration schemes. Examples of planned applications will also be described.status: accepte