True Direction Equilibrium Flux Method and its Application

Smith, Matthew Ross (2008). True Direction Equilibrium Flux Method and its Application PhD Thesis, School of Engineering, The University of Queensland.

       
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Author Smith, Matthew Ross
Thesis Title True Direction Equilibrium Flux Method and its Application
School, Centre or Institute School of Engineering
Institution The University of Queensland
Publication date 2008-06
Thesis type PhD Thesis
Supervisor Macrossan, Michael N.
Abdel-Jawad, Madhat
Subjects 290000 Engineering and Technology
Formatted abstract The True Direction Equilibrium Flux Method (TDEFM) is mathematically derived and ap¬plied to various flow problems. Rather than employing the conventional approach of calculating fluxes of mass, momentum and energy in a series of one dimensional fluxes across cell interfaces, TDEFM models the transportation of mass, momentum and energy based on the mechanism used by a direct solver (such as DSMC). The resulting expressions allow fluxes of mass, mo¬mentum and energy to be transfered from a specified source volume to a specified destination volume regardless of whether or not these regions share an adjacent interface. The fluxes of mass, momentum and energy calculated by TDEFM are the analytical solution to the free flight phase of a direct simulation when the flow is in thermal equilibrium and flow properties (such as density) are assumed uniform over each cell volume. The TDEFM fluxes are calculated by integrating the Maxwell-Boltzmann equilibrium distribution function over both velocity space and the physical volume of each cell. The primary advantage to this approach is that the TDEFM fluxes are true directional -fluxes of mass, momentum and energy can be transported in their physically correct direction and do not rely upon one dimensional reconstructions for flux calculation.
Direct solvers possess the ability to maintain gradients of density within each cell through simulation particle location. To increase the physical realism of TDEFM the fluxes are re-constructed using linear variations of density. The revised method, named Density TDEFM (DTDEFM), provides results which are closer to a direct solver in the equilibrium limit than conventional TDEFM without significantly increasing the computational expense. For com-pleteness further flux expressions are developed for the inclusion of linearly varying velocity, resulting in Velocity TDEFM (VTDEFM).
The capacity of TDEFM to capture unaligned flows on a regular grid is demonstrated in various one and two dimensional problems. The effects of using true directional fluxes are first demonstrated by testing the two dimensional radial blast wave and implosion problem. These results obtained show that the results obtained using true directional fluxes better capture the radial motion of gas on a regular cartesian grid when compared to other selected first order continuum solvers. The true directional fluxes were then used to simulate various hypersonic flow problems. The development of these true directional fluxes ultimately lead to the creation of FASTWAVE, a tool capable of predicting blast wave behaviour in city environments in a matter of minutes on a standard desktop PC or laptop. Finally, extensions to viscous flow using en route collisions, adaptive mesh refinement and the hybridisation of TDEFM with a BGK solver is discussed.


 
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