Micro-domain multi-scale flow simulation is one of the most difficult and unresolved problems in today's computational mathematics. Simulating micro-propulsion generated by the plasma flow from the micro-pulsed plasma thruster (PPT) is one of the examples. Flow in a micro-PPT is partially ionized collisional plasma exhibiting transition from continuum to rarefied (or non-equilibrium) regime. To successfully simulate such multi-scale flow, a novel stochastic hybrid algorithm combining direct simulation Monte Carlo (DSMC) method suitable for highly non-equilibrium flow regime and continuum methods in the rest of the domain for efficiency is proposed. Using the new algorithm, the study will focus on numerical modeling the internal flow of the micro-thruster. To the end, stochastic simulations are planned to optimize performance characteristics of the thruster such as specific impulse and thrust. The intellectual merit of the proposed activity lies in the development and analysis of new numerical algorithms and application of these algorithms for large scale simulations of multi-scale flow problems. Moreover, one significance of the proposed research is to build a stochastic interface between kinetic and continuum methods to exchange the statistical distribution instead of the spatial-temporal average. Proposed tools will be applied to study the micro-thruster to order to improve their performance by optimizing their geometry.

The proposed work will broadly extend the understanding of the behavior of multi-scale flows in many applications of current interest. It will assist in developing new micro-propulsion devices with improved efficiency, which is important for next generation micro-spacecrafts. Moreover, the methods to be developed can be applied to numerous applications in engineering, physics and biology including, but not limited to, hypersonic re-entry vehicles, thermo-fluids of fusion blankets and dissolution of a blood clot by ultrasound. Proposed work will continue and expand the PI?s educational outreach activities by building a strong collaboration between University of Notre Dame and Pacific Northwest National Laboratory and providing interdisciplinary training for students. An interdisciplinary training of undergraduate and graduate student training is planned.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
Standard Grant (Standard)
Application #
Program Officer
Leland M. Jameson
Project Start
Project End
Budget Start
Budget End
Support Year
Fiscal Year
Total Cost
Indirect Cost
University of Notre Dame
Notre Dame
United States
Zip Code