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

Abstract

A computationally efficient solution-adaptive finitevolume scheme is proposed and developed for obtaining timeinvariant multi-dimensional solutions of a novel maximum-entropybased, interpolative, 14-moment closure which provides a fully hyperbolic description of non-equilibrium transport phenomena in monatomic gases, including heat transfer. Unlike the maximumentropy closure on which it is based, the interpolative closure provides approximate closed-form expressions for the closing fluxes. A Godunov-type finite-volume with piecewise limited linear solution reconstruction is combined with an adaptive mesh refinement (AMR) algorithm permitting local refinement to obtain solutions to the governing hyperbolic system of moment equations on twodimensional, body-fitted, multi-block grids consisting of quadrilateral cells. Time-invariant solutions of the spatially-discretized moment equations are obtained by using an inexact Newton's method combined with a preconditioned Krylov subspace iterative method. In particular, the GMRES (Generalized Minimal RESidual) iterative method is combined with a Schwarz-type preconditioning strategy based on the multi-block grid in the iterative solution solution of linear equations at each Newton step. The application of the 14moment closure is considered for some canonical non-equilibrium flow problems, including subsonic flow around a circular-cylinder and a lid driven cavity flow. The predictive capabilities of the 14-moment interpolative closure are shown to surpass those of the regularized Gaussian closure, which models heat transfer through the addition of elliptic terms using a regularization technique applied to the low-order Gaussian closure. The 14-moment closure is also found to predict interesting non-equilibrium phenomena, such as counter-gradient heat transfer, a highly non-equilibrium phenomenon.