Efficient Simulation of Nonlinear Flows in Rarefied Gases

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The computation of gas flows is typically based on the Navier-Stokes equations for the velocity field combined with the energy balance and Fourier's law if the temperature field is of interest. However, these classical models are valid only for flows close to thermal equilibrium. For situations in rarefied gases or in microscopic settings the Navier-Stokes-Fourier system (NSF) is known to produce physically wrong results, so that they can not be used in these cases. Over the past years new continuum models have been developed on the bases of moment equations of the Boltzmann equation which extend the range of applicability of conventional fluid dynamics. One of these models is the Regularized 13-Moment system (R13) which forms a set of partial differential equations for density, velocity and temperature, as well as stress tensor and heat flux. In an earlier DFG project the R13 system has been successfully developed to a mature simulation tool for slow rarefied gas systems, like in microscopic settings.However, one of the main drawbacks of classical moment equations like the R13 system is the restriction to small perturbation like in slow, low Mach number processes. The mathematical reason can be found in the expansion technique used to approximate the velocity distribution function of the gas particles. The current project explores new ways to extend the use of moment equations to strongly nonlinear processes, exhibiting strong variations in velocity and temperature, like shock waves in hypersonics. During the project we will combine two modern approaches to reconstruct a distribution from moments: maximum likelihood/entropy estimation from statistics and the quadrature method of moments, introduced in multi-phase/multi-disperse flows. A successful and efficient reconstruction will allow to handle boundary conditions and to implement a numerical method easily. One application-inspired test case will consider flow impingement of satellite thrusters.