One key limiting factor to groundwater remediation is contaminant sequestered in pores whose contents do not mix well with the bulk flow. Mixing between well-connected (pores whose volume is flushed as water flows through the aquifer) and poorly connected pores (pores whose volume does not exchange readily when water flows through the aquifer) is of primary concern. Under steady flow, contaminants are effectively trapped in the poorly connected pores and are transferred only by molecular diffusion. This slow mixing process between pore types is a bottleneck to remediation. We present a novel rapidly pulsed pumping method that increases the mixing between these pore types. We do it in the context of pump-and-treat remediation because it is the most common remediation practice. In rapidly pulsed pumping, the increase in flow causes a deep sweep, which pushes the flow into poorly connected pores and sweeps out sequestered contaminants. The decrease in flow causes a vortex ejection, which causes the vortex within the poorly connected pore to emerge with contaminant. These actions are modeled with computational fluid mechanics to elucidate the individual mechanisms and determine how they function and interact. Cleanup of single and multiple poorly connected pore systems were simulated and show the acceleration possible. This technique can decrease the time and cost needed to remediate contaminated aquifers, which in the United States has been estimated to exceed $1 trillion. Since our rapidly pulsed pumping method enhances mixing between well-connected and poorly connected pores, it can be applied to other remediation schemes such as in situ methods.