Partially Penalized Immersed Finite Element Methods for Elliptic Interface Problems

This article presents new immersed finite element (IFE) methods for solving the popular second order elliptic interface problems on structured Cartesian meshes even if the involved interfaces have nontrivial geometries. These IFE methods contain extra stabilization terms introduced only at interface edges for penalizing the discontinuity in IFE functions. With the enhanced stability due to the added penalty, not only these IFE methods can be proven to have the optimal convergence rate in the H1-norm provided that the exact solution has sufficient regularity, but also numerical results indicate that their convergence rates in both the H1-norm and the L2-norm do not deteriorate when the mesh becomes finer which is a shortcoming of the classic IFE methods in some situations. Trace inequalities are established for both linear and bilinear IFE functions that are not only critical for the error analysis of these new IFE methods, but also are of a great potential to be useful in error analysis for other IFE methods

Thermal Performance Analysis of an Underground Closed Chamber with Human Body Heat Sources under Natural Convection

In this article, a combined experimental and numerical study has been performed to investigate the thermal performance of a mine refuge chamber (MRC) under natural convection. In the current study, a 20-hour heating experiment is carried out in a fifty-person MRC laboratory and the heat lamps are utilized to simulate the human heat loss. A new analytical model is proposed to predict the air temperature and validated against the experimental data. Sensitivity analysis is performed to further investigate the effects of the thermal parameters of the rock. Results indicated that: (1) two different air temperature increase stages, rapid and slow increase stages, are observed in the MRC; (2) A new analytical method for predicting the air temperature in MRC under natural convection is proposed, it shows that the air temperature increasing trend becomes slow with the increase of the thermal conductivity, density and specific heat capacity of the rock; (3) the surface heat transfer coefficient on the vertical walls reaches the largest and it increases linearly with air temperature.Peer reviewe

Controllable terahertz radiation from a linear-dipole-array formed by a two-color laser filament in air

We have demonstrated the effective control on carrier-envelope phase, angular distribution as well as peak intensity of a nearly single-cycle terahertz pulse emitted from a laser filament formed by two-color, the fundamental and the corresponding second harmonics, femtosecond laser pulses propagating in air. Experimentally, such control has been performed by varying the filament length and the initial phase difference between the two-color laser components. A linear-dipole-array model, including the descriptions of the both generation (via laser field ionization) and propagation of the emitted terahertz pulse, is proposed to present a quantitative interpretation of the observations. Our results contribute to the understanding of terahertz generation in a femtosecond laser filament and suggest a practical way to control the electric field of terahertz pulse for potential applications