The low energy beam transport (LEBT) system in the front-end of the Rare Isotope Accelerator (RIA) uses a 70 kV platform to pre-accelerate the ion beam from a 30 kV Electron Cyclotron Resonance (ECR) ion source, followed by an achromatic charge selection system. The selected beam is then pre-bunched and matched into the entrance of a Radio Frequency Quadrupole (RFQ) with a multi-harmonic buncher. To meet the beam power requirements for heavy ions, high current (several mA), multi-species beams will be extracted from the ECR. Therefore, it is crucial to control space charge effects in order to obtain the low emittance beam required for RIA. The PARMELA code is used to perform the LEBT simulations for the multi-species beams with 3D space charge calculations. The results of the beam dynamics simulations are presented, and the key issues of emittance growth in the LEBT and its possible compensation are discussed.