Molecular Line Emission from Multifluid Shock Waves. I. Numerical Methods and Benchmark Tests

TL;DR

This paper introduces a numerical scheme for simulating multifluid magnetohydrodynamic shock waves in interstellar clouds, validated through benchmark tests and exact solutions, advancing the modeling of astrophysical shock phenomena.

Contribution

The paper presents a novel operator splitting numerical scheme for multifluid MHD shocks, including benchmark tests and an exact Riemann problem solution for validation.

Findings

The scheme accurately models multifluid shock wave dynamics.

Benchmark tests confirm the scheme's convergence and reliability.

The exact solution aids in validating numerical results.

Abstract

We describe a numerical scheme for studying time-dependent, multifluid, magnetohydrodynamic shock waves in weakly ionized interstellar clouds and cores. Shocks are modeled as propagating perpendicular to the magnetic field and consist of a neutral molecular fluid plus a fluid of ions and electrons. The scheme is based on operator splitting, wherein time integration of the governing equations is split into separate parts. In one part independent homogeneous Riemann problems for the two fluids are solved using Godunov's method. In the other equations containing the source terms for transfer of mass, momentum, and energy between the fluids are integrated using standard numerical techniques. We show that, for the frequent case where the thermal pressures of the ions and electrons are << magnetic pressure, the Riemann problems for the neutral and ion-electron fluids have a similar mathematical structure which facilitates numerical coding. Implementation of the scheme is discussed and several benchmark tests confirming its accuracy are presented, including (i) MHD wave packets ranging over orders of magnitude in length and time scales; (ii) early evolution of mulitfluid shocks caused by two colliding clouds; and (iii) a multifluid shock with mass transfer between the fluids by cosmic-ray ionization and ion-electron recombination, demonstrating the effect of ion mass loading on magnetic precursors of MHD shocks. An exact solution to a MHD Riemann problem forming the basis for an approximate numerical solver used in the homogeneous part of our scheme is presented, along with derivations of the analytic benchmark solutions and tests showing the convergence of the numerical algorithm.