Application of a Maximum-Entropy-Based 14-Moment Closure for Multi-Dimensional Non-Equilibrium Flows

Abstract

The predictive capabilities of a new, 14-moment, maximum-entropy-based, interpolative closure are explored for multi-dimensional non-equilibrium flows with heat transfer. Unlike the maximum-entropy closure on which it is based, the interpolative closure provides closed-form expressions for the closing fluxes. While still presenting singular solutions in regions of realizable moment space, the interpolative closure proves to have a large region of hyperbolicity while remaining tractable. Furthermore, its singular nature is deemed advantageous for practical simulations. An implicit finite-volume procedure is proposed and described for the numerical solution of the 14-moment closure on two-dimensional computational domains, followed by a presentation and discussion of the results of a numerical dispersion analysis. Multi-dimensional applications of the closure are then examined for several canonical flow problems in order to provide an assessment of the capabilities of this novel closure for a range of non-equilibrium flows. The computational performance of the implicit solver is compared to a semi-implicit method. The predictive capabilities of the 14-moment interpolative closure were found to surpass those of the 10-moment Gaussian closure. It was also found to predict interesting non-equilibrium phenomena, such as counter-gradient heat flux. The implicit solver showed improved computational performance compared to the previously studied semi-implicit technique.

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

“…The simple Lax-Friedrichs method has been proficiently employed in the past to solve maximum-entropy systems, 22 but it is overwhelmingly diffusive in highly rarefied and supersonic conditions, where the Junk line is approached closely, and the fastest wave speeds become very large. The HLL scheme has also been employed in previous maximum-entropy simulations, 46 but for relatively high-collisional cases, and employing crude approximations for the eigenvalues, unsuitable for supersonic rarefied conditions.…”

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.…”

Efficient solution-adaptive finite-volume scheme for time-invariant multi-dimensional solutions of maximum-entropy-based 14-moment closure for non-equilibrium gases

“…Nevertheless more recently, interpolative-type, maximum-entropy-based, 5-moment (onedimensional gas) and 14-moment (three-dimensional gas) closures, initially investigated by McDonald and Groth [6], and expanded upon by McDonald and Torrilhon [16], have been proposed that successfully navigate the aforementioned problems. This has allowed the successful application of the interpolative variants of the super-quadratic maximum-entropy closures to a number of two-dimensional non-equilibrium flows, demonstrating their promise for transition-regime nonequilibrium flows [17]- [19].…”