A Unified Multidimensional Hybrid Gaskinetic BGK method using Cartesian Grid for Nonequilibrium and Chemically Reacting Flows

A consistent time-accurate Hybrid gaskinetic Bhatnagar-Gross-Krook (BGK) method (H-BGK), valid in the full Knudsen number (Kn) range, is proposed using Cartesian grid as a 3D tool to handle hypersonic aerothermodynamics from continuum to thermochemical nonequilibrium and ionized/plasma flows.  H-BGK method is to provide automated sub-domain solutions by direct BGK method and the gaskinetic BGK method of Xu (BGKX) in the high and low Kn regimes respectively.  Direct BGK employs the Shakov model using quadratures, i.e., values of the distribution function at certain discrete velocities being used in the integration, and high-order upwind scheme for its solution. The BGKX solver is a finite volume method, proven applicable for thermochemical nonequilibrium flows with accurate heat rate prediction.  The Cartesian method proposed is a Gridless Boundary Condition Cartesian (GBCC) method due to Feng Liu, which is a grid-automated scheme with built-in multigrid to accelerate convergence and has proven applicable to unsteady/steady 3D flows.   Phase I will validate H-BGK solutions with that of DSMC in terms of pressures and heat rates for cylinders and blunt cones at various Knudsen numbers. Phase II will fully develop the H-BGK solver in 3D with GBCC in chemically-reacting and ionization flows, boundary layer resolutions and aerothermodynamic prediction capability. BENEFIT: The developed hybrid BGK (H-BGK) solver with a Gridless Boundary Condition Cartesian (GBCC) grid framework can be used for hypersonic applications from continuum to rarefied flow regimes for thermochemical nonequilibrium effects up to ionization/plasma flows. H-BGK solver can generate accurate aerodynamic forces and heat rates, and GBCC will largely relief users heavy burden on meshing.   Typical applications are for launch vehicles in space access, entry command module and ballutes in atmospheric entry ; plume flows in chemical engines or rockets.  Civilian dual-use applications include micro flows and micro heat transfer, such as those inside Micro- or Nano- Electro-Mechanical Systems, MEMS/NEMS.  Examples include the heat flow rate prediction of microchips inside a vacuum packaged enclosure, gas flows through micro-thrusters, gas phase chemical sensors, lab-on-a-chip.   Potential customers include the Air Force, DoD, NASA and private sectors using the solver for hypersonic vehicle design/analysis. Civil applications will provide design/analysis methods for MEMs, and biomedical equipments.