We present a three-dimensional dissipative particle dynamics model of DNA electrophoretic flow that captures both DNA stochastic motion and hydrodynamics without requiring expensive molecular dynamics calculations. This model enables us to efficiently and simultaneously simulate DNA electrophoretic flow and local EOF (generated by counterions near the DNA backbone), in mesoscale (similar to mu m) fluidic devices. Our model is used to study the electrophoretic separation of long DNA chains under entropic trapping conditions [Han and Craighead, Science 2000, 288, 1026-1029]. Our simulation results are in good agreement with experimental data for realistic geometries (tapered walls) and reveal that wall tapering in entropic traps has a profound impact in the DNA trapping behavior, an effect which was largely ignored in previous modeling.