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We describe a numerical scheme for studying time-dependent, multifluid,magnetohydrodynamic shock waves in weakly ionized interstellar clouds andcores. Shocks are modeled as propagating perpendicular to the magnetic fieldand consist of a neutral molecular fluid plus a fluid of ions and electrons.The scheme is based on operator splitting, wherein time integration of thegoverning equations is split into separate parts. In one part independenthomogeneous Riemann problems for the two fluids are solved using Godunov'smethod. In the other equations containing the source terms for transfer ofmass, momentum, and energy between the fluids are integrated using standardnumerical techniques. We show that, for the frequent case where the thermalpressures of the ions and electrons are << magnetic pressure, the Riemannproblems for the neutral and ion-electron fluids have a similar mathematicalstructure which facilitates numerical coding. Implementation of the scheme isdiscussed and several benchmark tests confirming its accuracy are presented,including (i) MHD wave packets ranging over orders of magnitude in length andtime scales; (ii) early evolution of mulitfluid shocks caused by two collidingclouds; and (iii) a multifluid shock with mass transfer between the fluids bycosmic-ray ionization and ion-electron recombination, demonstrating the effectof ion mass loading on magnetic precursors of MHD shocks. An exact solution toa MHD Riemann problem forming the basis for an approximate numerical solverused in the homogeneous part of our scheme is presented, along with derivationsof the analytic benchmark solutions and tests showing the convergence of thenumerical algorithm.

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