Multi-dimensional validation of a maximum-entropy-based interpolative moment closure

Abstract

Articles you may be interested inComparison of maximum entropy and quadrature-based moment closures for shock transitions prediction in onedimensional gaskinetic theory AIP Conf.Abstract. The performance of a novel maximum-entropy-based 14-moment interpolative closure is examined for multidimensional flows via validation of the closure for several established benchmark problems. Despite its consideration of heat transfer, this 14-moment closure contains closed-form expressions for the closing fluxes, unlike the maximum-entropy models on which it is based. While still retaining singular behaviour in some regions of realizable moment space, the interpolative closure proves to have a large region of hyperbolicity while remaining computationally tractable. Furthermore, the singular nature has been shown to be advantageous for practical simulations. The multi-dimensional cases considered here include Couette flow, heat transfer between infinite parallel plates, subsonic flow past a circular cylinder, and lid-driven cavity flow. The 14-moment predictions are compared to analytical, DSMC, and experimental results as well the results of other closures. For each case, a range of Knudsen numbers are explored in order to assess the validity and accuracy of the closure in different regimes. For Couette flow and heat transfer between flat plates, it is shown that the closure predictions are consistent with the expected analytical solutions in all regimes. In the cases of flow past a circular cylinder and lid-driven cavity flow, the closure is found to give more accurate results than the related lower-order maximum-entropy Gaussian and maximum-entropy-based regularized Gaussian closures. The ability to predict important non-equilibrium phenomena, such as a counter-gradient heat flux, is also established.

Numerical simulation of rarefied supersonic flows using a fourth-order maximum-entropy moment method with interpolative closure

“…The rationale behind this approximation is that, if k is large enough, the simulation should remain stable. This approach has the benefit of being simple, and was shown to be profitable in a number of conditions (see for instance 68 ). However, this approximation is not suitable for the present work, where the high rarefaction and supersonic speeds let the system depart significantly from equilibrium and also approach the Junk subspace.…”

A 14-moment maximum-entropy description of electrons in crossed electric and magnetic fields

“…However, recent developments have provided approximated interpolative approaches to the entropy maximisation problem, which allow for an agile and affordable solution to be found for selected systems of equations, 38 and their application to multi-dimensional non-equilibrium gaseous flows has yielded very promising results. 39,40 In this work, we consider a 14-moment maximumentropy description for the electron population. 24,38,41 First, in Section II we discuss the kinetic equation and provide a brief description of the maximum-entropy framework, together with the system of 14 moments adopted here.…”

Reconstruction of Electron and Ion Distribution Functions in a Magnetotail Reconnection Diffusion Region

“…Journal of Geophysical Research: Space Physics remaining quantities to close the fluid equations (McDonald, 2016;McDonald & Torrilhon, 2013;Tensuda et al, 2016). It has also been shown that there can exist physically realizable states which cannot be described by Equation 7, though it is possible to guarantee realizability by slightly modifying the distribution (Groth & McDonald, 2009;Junk, 1998;McDonald & Groth, 2013;Schaerer & Torrilhon, 2015).…”