Regensburg 2022 – wissenschaftliches Programm

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VA: Fachverband Vakuumphysik und Vakuumtechnik

VA 1: Rarefied gas dynamics and novel numerical approaches

VA 1.3: Vortrag

Montag, 5. September 2022, 10:50–11:30, H12

The Regularized 13-Moment Equations for Rarefied Gas Simulations — •Manuel Torrilhon — RWTH Aachen University

The Regularized 13-Moment-Equations (R13) are using moment approximations for the Boltzmann equation in kinetic gas theory to describe gas flows when the Knudsen number - the ratio between mean free path and observation scale - becomes significant. Classical fluid theories like the constitutive laws of Navier-Stokes and Fourier are valid only close to equilibrium and fail for processes at Knudsen numbers as low as 0.05 because there are not sufficient particle collisions within the gas to maintain equilibrium.

The derivation of the R13-equations relies on the combination of moment approximations and asymptotic expansions in kinetic gas theory. The system has been shown to be stable and of high asymptotic accuracy yet using only a relatively small set of variables, namely density, velocity, temperature, stress deviator and heat flux - in total 13 fields. It has been demonstrated to succeed on the prediction of various non-equilibrium processes like shock waves or channel flows with Knudsen layers. The system of equations also exhibits desirable mathematical features like an entropy and is easy to use in numerical simulations. An overview of the equations and their features can be found in the review in Ann. Rev. Fluid Mech. 48, (2016), 429-458.

This talk will introduce the model and discuss recent developments like the efficient implementation in finite element frameworks, polyatomic collision models, and nonlinear extensions.