Computer Physics Communications 164 (2004) 209–213 www.elsevier.com/locate/cpc The particle-continuum method: an algorithmic unification of particle-in-cell and continuum methods ✩ Srinath Vadlamani ∗ , Scott E. Parker, Yang Chen, Charlson Kim 1 Center for Integrated Plasma Studies, University of Colorado, Boulder, CO 80309, USA Available online 24 July 2004 Abstract A new numerical algorithm that encompasses both the δf particle-in-cell (PIC) method and a continuum method has been developed, which is an extension to Denavit’s [J. Comput. Phys. 9 (1972) 75] original “hybrid” method. In this article we describe this new Particle-Continuum algorithm in general, and we note our methods of interpolation. The issue of phase space convergence of this algorithm is discussed. We analyze the induced numerical diffusion of such an algorithm and compare theory with results. We also created a simple problem that demonstrates this algorithm solves the “growing weight” problem.  2004 Elsevier B.V. All rights reserved. PACS: 07.05.T; 52.65; 52.35; 52.55 Keywords: Plasma; Kinetic; Vlasov; Particle; Simulation 1. Introduction Expanding upon Denavit’s hybrid method [1] and Batischev’s PIC–Vlasov method [2–4] we have cre- ated a new algorithm that can vary between a contin- uum and δf PIC method. A primary distinction of the method presented here is the use of the δf = f − f 0 to describe the distribution function [11]. This study is of value for two reasons: (1) It makes a connec- tion between the particle-based δf and continuum ✩ This research is supported by the VIGRE Grant #DMS- 9810751. * Corresponding author. E-mail address: srinath.vadlamani@colorado.edu (S. Vadlamani). URL: http://srinath.colorado.edu (S. Vadlamani). 1 Currently at UW Madison. methods for solving kinetic equations thereby allow- ing detailed comparisons of the two methods. (2) The method solves the “growing weight problem” in δf particle simulations of plasma turbulence as detailed by Krommes and Hu [5]. The basic algorithm is es- sentially a variant of the δf method. A simple de- scription of the algorithm is as follows: (1) load par- ticles (or characteristics) on a uniform lattice in phase space. The loading need not be uniform, but it greatly simplifies the algorithm, (2) advance the characteris- tics M time steps, using the usual δf PIC algorithm which involves a grid interpolation, deposition, then field solve all on a spatial grid, (3) every M time steps, deposit δf on the phase space grid, then reset the par- ticle phase space coordinates back to their initial value on the phase space lattice. Also, reset the particle value of δf to the phase space grid value. 0010-4655/$ – see front matter  2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cpc.2004.06.031