Stability analysis of the numerical Method of characteristics applied to a class of energy-preserving systems. Part II: Nonreflecting boundary conditions

TL;DR

This paper investigates how nonreflecting boundary conditions influence the stability of the Method of Characteristics when applied to energy-preserving systems, revealing that boundary conditions can significantly alter stability outcomes.

Contribution

It demonstrates that non-periodic boundary conditions can stabilize certain MoC schemes, contradicting previous assumptions, and explains the underlying mechanisms affecting stability.

Findings

Nonreflecting BC can stabilize some MoC schemes.

Stability can depend on the choice of ODE solver within MoC.

The mechanism behind stability changes is clarified.

Abstract

We show that imposition of non-periodic, in place of periodic, boundary conditions (BC) can alter stability of modes in the Method of characteristics (MoC) employing certain ordinary-differential equation (ODE) numerical solvers. Thus, using non-periodic BC may render some of the MoC schemes stable for most practical computations, even though they are unstable for periodic BC. This fact contradicts a statement, found in some literature, that an instability detected by the von Neumann analysis for a given numerical scheme implies an instability of that scheme with arbitrary (i.e., non-periodic) BC. We explain the mechanism behind this contradiction. We also show that, and explain why, for the MoC employing some other ODE solvers, stability of the modes may be unaffected by the BC.