In order to overcome limitations on the simulation time step for fluid transport simulations of high density plasma discharges, the dielectric relaxation scheme (DRS) was developed. By imitating a realistic and physical shielding process of electric field perturbation, DRS overcomes the dielectric limitation on simulation time step. However, the electric field was obtained by assuming the drift-diffusion approximation for both the electrons and ions. Although the drift-diffusion expressions are good approximations, the inertial term cannot be neglected in the ion momentum equation for low pressure. Therefore, in this work, we developed the extended dielectric relaxation scheme (EDRS) by introducing an effective electric field. Similar to DRS, EDRS is limited to quasi-neutral plasma with zero current, i.e. EDRS is applicable when the local ambipolarity is satisfied. In order to validate EDRS, two-dimensional fluid simulations for inductively coupled plasma discharges were performed. The simulation results are then compared with experimental measurements by using a Langmuir probe. (C) 2016 Elsevier B.V. All rights reserved.