• Abstract

Extended hydrodynamic models for carrier transport are derived from the semiconductor Boltzmann equation with relaxation time approximation of the scattering term, by using the globally hyperbolic moment method and the moment-dependent relaxation time. Incorporating the microscopic relaxation time and the applied voltage bias, a formula is proposed to determine the relaxation time for each moment equation, which sets different relaxation rates for different moments such that higher moments damp faster. The resulting models would give more satisfactory results of macroscopic quantities of interest with a high-order convergence to those of the underlying Boltzmann equation as the involved moments increase, in comparison to the corresponding moment models using a single relaxation time. In order to simulate the steady states efficiently, a multigrid solver is developed for the derived moment models. Numerical simulations of an $n^+-n-n^+$ silicon diode are carried out to demonstrate the validation of the presented moment models, and the robustness and efficiency of the designed multigrid solver.

• Abstract

We describe a relativistic semi-Lagrangian scheme for the numerical solution of the relativistic Vlasov-Maxwell system. The implementation strategy on a modern non-unified memory access (NUMA) architecture using the OpenMP framework is discussed. We demonstrated that close to perfect scaling can be obtained on modern many-core, multi-socket systems. Application of this code to the problem of relativistic generation of high-harmonic laser radiation is demonstrated. The results are compared to particle-in-cell (PIC) simulations, indicating in particular that for warm plasma the Vlasov simulation is superior. We discuss the impact of plasma temperature on the radiation spectrum and show that the efficiency of harmonic generation depends on the plasma temperature.

• Abstract

In the paper, we focus on atom diffusion behavior in Ni-based superalloys, which have important applications in the aero-industry. Specifically, the expressions of the key physical parameter – transition rate (jump rate) in the diffusion can be given from the diffusion theory in solids and the kinetic Monte Carlo (KMC) method, respectively. The transition rate controls the diffusion process and is directly related to the energy of vacancy formation and the energy of migration of atom from density functional theory (DFT). Moreover, from the KMC calculations, the diffusion coefficients for Ni and Al atoms in the γ phase (Ni matrix) and the $γ^′$ phase (intermetallic compound Ni₃Al) of the superalloy have been obtained. We propose a strategy of time stepping to deal with the multi-time scale issues. In addition, the influence of temperature and Al concentration on diffusion in dilute alloys is also reported.

• Abstract

The modified ghost fluid method (MGFM), due to its reasonable treatment for ghost fluid state, has been shown to be robust and efficient when applied to compressible multi-medium flows. Other feasible definitions of the ghost fluid state, however, have yet to be systematically presented. By analyzing all possible wave structures and relations for a multi-medium Riemann problem, we derive all the conditions to define the ghost fluid state. Under these conditions, the solution in the real fluid region can be obtained exactly, regardless of the wave pattern in the ghost fluid region. According to the analysis herein, a practical ghost fluid method (PGFM) is proposed to simulate compressible multi-medium flows. In contrast with the MGFM where three degrees of freedom at the interface are required to define the ghost fluid state, only one degree of freedom is required in this treatment. However, when these methods proved correct in theory are used in computations for the multi-medium Riemann problem, numerical errors at the material interface may be inevitable. We show that these errors are mainly induced by the single-medium numerical scheme in essence, rather than the ghost fluid method itself. Equipped with some density-correction techniques, the PGFM is found to be able to suppress these unphysical solutions dramatically.

• Abstract

In this work two particle methods are studied in the context of viscous flows. The first one is a Vortex Particle Method, called Diffused Vortex Hydrodynamics (DVH), recently developed to simulate complex viscous flows at medium and high Reynolds regimes. This method presents some similarities with the SPH model and its Lagrangian meshless nature, even if it is based on a different numerical approach. Advantages and drawbacks of the two methods have been previously studied in Colagrossi et al. [1] from a theoretical point of view and in Rossi et al. [2], where these particle methods have been tested on selected benchmarks. Further investigations are presented in this article highlighting analogies and differences between the two particle models.

• Abstract

We investigate theoretically the field-free orientation of CO molecules induced by a single-cycle THz laser pulse train. It is shown that the molecular orientation can be obviously enhanced by applying the pulse train. The laser intensity and pulse number have some effects on the molecular orientation. The high degree of field-free molecular orientation $|$$〈$cos$θ$$〉$$|$_max=0.9246 is obtained at temperature $T$=0 K. The variations of the maximum orientation degree with the experimentally available pulse number and peak intensity are given. Temperature $T$ has a considerable influence on the field-free molecular orientation. The maximal field-free molecular orientation at $T$=0, 10, 20 and 30 K for $N$=14 and $E_0$=1.8 MV/cm are $|$$〈$cos$θ$$〉$$|$_max=0.9188, 0.7338, 0.6055 and 0.5154 in order, and the corresponding effective duration times of molecular orientation are $∆t$=0.759, 0.432, 0.297 and 0.117 ps.

• Abstract

We review, implement, and compare numerical integration schemes for spatially bounded diffusions stopped at the boundary which possess a convergence rate of the discretization error with respect to the time step $h$ higher than $\mathcal{O}$$(√h)$. We address specific implementation issues of the most general-purpose of such schemes. They have been coded into a single Matlab program and compared, according to their accuracy and computational cost, on a wide range of problems in up to R⁴⁸. The paper is self-contained and the code will be made freely downloadable.

• Abstract

We present a simple, accurate method for computing singular or nearly singular integrals on a smooth, closed surface, such as layer potentials for harmonic functions evaluated at points on or near the surface. The integral is computed with a regularized kernel and corrections are added for regularization and discretization, which are found from analysis near the singular point. The surface integrals are computed from a new quadrature rule using surface points which project onto grid points in coordinate planes. The method does not require coordinate charts on the surface or special treatment of the singularity other than the corrections. The accuracy is about O($h^3$), where $h$ is the spacing in the background grid, uniformly with respect to the point of evaluation, on or near the surface. Improved accuracy is obtained for points on the surface. The treecode of Duan and Krasny for Ewald summation is used to perform sums. Numerical examples are presented with a variety of surfaces.

• Abstract

We study the exciton diffusion in organic semiconductors from a macroscopic viewpoint. In a unified way, we conduct the equivalence analysis between Monte-Carlo method and diffusion equation model for photoluminescence quenching and photocurrent spectrum measurements, in both the presence and the absence of Förster energy transfer effect. Connections of these two models to Stern-Volmer method and exciton-exciton annihilation method are also specified for the photoluminescence quenching measurement.

• Abstract

As an exploratory study for structural deformation and thermodynamic response induced by spacecraft reentry aerodynamic force and thermal environment, a finite element algorithm is presented on the basis of the classic Fourier heat conductive law to simulate the dynamic thermoelasticity coupling performance of the material. The Newmark method and Crank-Nicolson scheme are utilized to discretize the dynamic thermoelasticity equation and heat conductive equation in the time domain, respectively, and the unconditionally stable implicit algorithm is constructed. Four types of finite-element computing schemes are devised and discussed to solve the thermodynamic coupling equation, all of which are implemented and compared in the computational examples including the one-dimensional transient heat conduction in considering and not considering the vibration, the transient heat flow for the infinite cylinder, and the dynamic coupling thermoelasticity around re-entry flat plate from hypersonic aerothermodynamic environment. The computational results show that the transient responses of temperature and displacement field generate lag phenomenon in case of considering the deformation effect on temperature field. Propagation, rebounding, attenuation and stabilized phenomena of elastic wave are also observed by the finite-element calculation of thermodynamic coupling problem considering vibration and damping, and the oscillation of the temperature field is simultaneously induced. As a result, the computational method and its application research platform have been founded to solve the transient thermodynamic coupling response problem of the structure in strong aerodynamic heating and force environment. By comparing various coupling calculations, it is demonstrated that the present algorithm could give a correct and reliable description of transient thermodynamic responses of structure, the rationality of the sequentially coupling method in engineering calculation is discussed, and the bending deformation mechanism produced by the thermodynamic coupling response from windward and leeward sides of flying body is revealed, which lays the foundation in developing the numerical method to solve material internal temperature distribution, structural deformation, and thermal damage induced by spacecraft dynamic thermoelasticity coupling response under uncontrolled reentry aerothermodynamic condition.

• Abstract

The static shape of drop under electrowetting actuation is well studied and recent electrowetting theory and experiments confirm that the local contact angle (microscopic angle) is unaffected while the apparent contact angle (macroscopic angle) is characterized by the Lippmann-Young equation. On the other hand, the evolution of the drop motion under electrowetting actuation has received less attention. In this paper, we investigate the motion of a conducting water drop on an electrowetting device (EWD) using the level set method. We derive a contact line two-phase flow model under electrowetting actuation using energy dissipation by generalizing an existing contact line model without the electric field. Our model is consistent with the static electrowetting theory as the dynamic contact angle satisfies the static Young's equation under equilibrium conditions. Our steady state results show that the apparent contact angle predicted by our model satisfies the Lippmann-Young's relation. Our numerical results based on the drop maximum deformation agree with experimental observations and static electrowetting theory. Finally, we show that for drop motion our results are not as good due to the difficulty of computing singular electric field accurately. Nonetheless, they provide useful insights and a meaningful first step towards the understanding of the drop dynamics under electrowetting actuation.