Grad's 13-moment equations describe transport in mildly rarefied gases well, but are not properly embedded into nonequilibrium thermodynamics since they accompanied by a formulation of the second law. In this work, Grad-13 framework GENERIC (general equation for reversible–irreversible coupling), which demands additional contributions to guarantee thermodynamic structure. As building blocks, we...

This paper studies an alternative bias correction for the M-estimator, which is obtained by correcting the moment equations in the spirit of Firth (1993). In particular, this paper compares the stochastic expansions of the analytically-bias-corrected estimator and the alternative estimator and finds that the third-order stochastic expansions of these two estimators are identical. This implies t...

The spherical harmonics (PN) method is widely used in solving the neutron transport equation, but it has some disadvantages. One of them omes from the complexity of the PN equations. Another one comes from the difficulty of dealing with the vacuum boundary condition exactly. In his paper, the PN method is applied to the self-adjoint angular flux (SAAF) neutron transport equation and a set of PN...

In this paper at first introduced constituent equations for piezoelectric and then by the help of this equations, internal energy of hinged-hinged piezoelectric multilayer beam was computed. Then by the principle of minimum potential energy and Rayleigh -Ritz method the bending curvature equation of hinged-hinged piezoelectric multilayer beam under concentrated moment, concentrated force, unifo...

We present numerical calculations of spherically symmetric radiative transport using a two-moment (P-1) method with a two-dimensional non-linear closure on the Eddington factor. The stationary state solutions contain a critical point. We demonstrate that the two-moment equations with a non-linear closure are well behaved. The solutions are physically acceptable , regular and accurate.

Moment closures of gaskinetic theory offer a method for the prediction of non-equilibrium flows which have a wider range of validity than standard continuum methods, such as solution of the Navier-Stokes equations, and can be much more computationally efficient than particle-based techniques, such as Direct Simulation Monte Carlo (DSMC). Moment methods yield systems of first-order partial diffe...

This is the ®rst in a series of two papers generated from a study on net-section-collapse (NSC) analysis of circumferentially cracked pipes. In this paper (part I), a generalized NSC method is presented to predict the maximum moment of a circumferentially cracked pipe with a variable-depth internal surface crack subject to combined bending and tension (pressure-induced) loads. Two sets of equat...

The effects of a two-dimensional periodic dielectric substrate on the performance of a microstripfed wide slot antenna are investigated. The microstrip-feed and wide slot is placed on opposite sides of the periodic dielectric substrate. Method of Moment calculations using volume integral equations is employed to determine the effects of the substrate. It is proposed that by introducing a period...

The entropy-based moment method is a well-known discretization for the velocity variable in kinetic equations which has many desirable theoretical properties but difficult to implement with high-order numerical methods. regularized was recently introduced remove one of main challenges implementation method, namely requirement realizability solution. In this work we use relative entropy prove co...

We present an enhanced moment-closure approximation to the finiteextensiblenonlinear-elastic (FENE) models of polymeric fluids. This new moment-closure method involves the perturbation of the equilibrium probability distribution function (PDF), which takes into account of the drastic split into two spikes and centralized behavior under the large macroscopic flow effects. The resulting macroscop...