A Two-Fluid Method for Ambipolar Diffusion
  We present a semi-implicit method for isothermal two-fluid ion-neutral ambipolar drift that is second-order accurate in space and time. The method has been implemented in the RIEMANN code for astrophysical fluid dynamics. We present four test problems that show the method works and correctly tracks the propagation of MHD waves and the structure of two-fluid C-shocks. The accurate propagation of MHD waves in the two-fluid approximation is shown to be a stringent test of the algorithm. We demonstrate that highly accurate methods are required in order to properly capture the MHD wave behaviour in the presence of ion-neutral friction. 
David A. Tilley and Dinshaw S. Balsara