As applications approach extreme scales, data staging and in-situ/in-transit processing have been proposed to address the data challenges and improve scientific discovery. However, further research is necessary in order to understand how growing data sizes from data intensive simulations coupled with the limited DRAM capacity in High End Computing systems will impact the effectiveness of this approach. Moreover, the complex and dynamic data exchange patterns exhibited by the workflows coupled with the varied data access behaviors make efficient data placement within the staging area challenging. In this paper, we explore how we can use deep memory levels for data staging and develop a multi-tiered data staging method that spans both DRAM and solid state disks (SSD). This approach allows us to support both code coupling and data management for data-intensive simulation workflows. We also show how adaptive application-aware data placement mechanisms can dynamically manage and optimize data placement vertically across the DRAM and SSD storage levels and horizontally across different staging nodes in this multi-tiered data staging method. We present an experimental evaluation of our approach using two OLCF resources: an Infiniband cluster (Sith) and a Cray XK7 system (Titan), and using combustion (S3D) and fusion (XGC1) simulations. The evaluation results demonstrate that our approach can effectively improve data access performance and overall efficiency of coupled scientific workflows.