On the Courant-Friedrichs-Lewy condition for numerical solvers of the coagulation equation

TL;DR

This paper analyzes the stability conditions for numerical solvers of the coagulation equation in astrophysics, revealing that traditional CFL conditions are overly restrictive and proposing a new, less stringent stability criterion.

Contribution

The authors derive a novel stability condition for explicit solvers of the coagulation equation by analyzing it in Laplace space, improving simulation efficiency.

Findings

Traditional CFL conditions are overly restrictive for coagulation equations.

Laplace space analysis provides insights into stability criteria.

Proposed stability condition reduces computational constraints.

Abstract

Evolving the size distribution of solid aggregates challenges simulations of young stellar objects. Among other difficulties, generic formulae for stability conditions of explicit solvers provide severe constrains when integrating the coagulation equation for astrophysical objects. Recent numerical experiments have recently reported that these generic conditions may be much too stringent. By analysing the coagulation equation in the Laplace space, we explain why this is indeed the case and provide a novel stability condition which avoids time over-sampling.