Multigrid solver for axisymmetrical 2D fluid equations

TL;DR

This paper presents an efficient multigrid algorithm for solving steady axisymmetrical 2D fluid equations, enabling rapid solutions on large grids and facilitating hybrid code development for DC discharges.

Contribution

The paper introduces a multigrid solver tailored for axisymmetrical 2D fluid equations, optimizing computational efficiency and handling nonlinearity through multi-level grid extrapolation.

Findings

Achieved solutions on 256x256 grids in minutes.

Used multilevel grids to mitigate nonlinearity time constraints.

Demonstrated potential for hybrid code applications in plasma physics.

Abstract

We have developed an efficient algorithm for steady axisymmetrical 2D fluid equations. The algorithm employs multigrid method as well as standard implicit discretization schemes for systems of partial differential equations. Linearity of the multigrid method with respect to the number of grid points allowed us to use $256\times 256$ grid, where we could achieve solutions in several minutes. Time limitations due to nonlinearity of the system are partially avoided by using multi level grids(the initial solution on $256\times 256$ grid was extrapolated steady solution from $128\times 128$ grid which allowed using "long" integration time steps). The fluid solver may be used as the basis for hybrid codes for DC discharges.