On the lattice Boltzmann method for phonon transport

The lattice Boltzmann method is a discrete representation of the Boltzmann transport equation that has been employed for modeling transport of particles of different nature. In the present work, we describe the lattice Boltzmann methodology and implementation techniques for the phonon transport modeling in crystalline materials. We show that some phonon physical properties, e.g., mean free path and group velocity, should be corrected to their effective values for one- and two-dimensional simulations, if one uses the isotropic approximation. We find that use of the D2Q9 lattice for phonon transport leads to erroneous results in transient ballistic simulations, and the D2Q7 lattice should be employed for two-dimensional simulations. Furthermore, we show that at the ballistic regime, the effect of direction discretization becomes apparent in two dimensions, regardless of the lattice used. Numerical methodology, lattice structure, and implementation of initial and different boundary conditions for the D2Q7 lattice are discussed in detail.     

Numerical modeling of transient two-dimensional viscoelastic waves

This paper deals with the numerical modeling of transient mechanical waves in linear viscoelastic solids. Dissipation mechanisms are described using the generalized Zener model. No time convolutions are required thanks to the introduction of memory variables that satisfy local-in-time differential equations. By appropriately choosing the relaxation parameters, it is possible to accurately describe a large range of materials, such as solids with constant quality factors. The evolution equations satisfied by the velocity, the stress, and the memory variables are written in the form of a first-order system of PDEs with a source term. This system is solved by splitting it into two parts: the propagative part is discretized explicitly, using a fourth-order ADER scheme on a Cartesian grid, and the diffusive part is then solved exactly. Jump conditions along the interfaces are discretized by applying an immersed interface method. Numerical experiments of wave propagation in viscoelastic and fluid media show the efficiency of this numerical modeling for dealing with challenging problems, such as multiple scattering configurations.     

Point-wise hierarchical reconstruction for discontinuous Galerkin and finite volume methods for solving conservation laws

We develop a new hierarchical reconstruction (HR) method  and  for limiting solutions of the discontinuous Galerkin and finite volume methods up to fourth order of accuracy without local characteristic decomposition for solving hyperbolic nonlinear conservation laws on triangular meshes. The new HR utilizes a set of point values when evaluating polynomials and remainders on neighboring cells, extending the technique introduced in Hu, Li and Tang [9]. The point-wise HR simplifies the implementation of the previous HR method which requires integration over neighboring cells and makes HR easier to extend to arbitrary meshes. We prove that the new point-wise HR method keeps the order of accuracy of the approximation polynomials. Numerical computations for scalar and system of nonlinear hyperbolic equations are performed on two-dimensional triangular meshes. We demonstrate that the new hierarchical reconstruction generates essentially non-oscillatory solutions for schemes up to fourth order on triangular meshes.     

GPU accelerated CESE method for 1D shock tube problems

In the present study, a GPU accelerated 1D space–time CESE method is developed and applied to shock tube problems with and without condensation. We have demonstrated how to implement the CESE algorithm to solve 1D shock tube problems using an older generation GPU (the NVIDIA 9800 GT) with relatively limited memory. To optimize the code performance, we used Shared Memory and solved the inter-Block boundary problem in two ways, namely the branch scheme and the overlapping scheme. The implementations of these schemes are discussed in detail and their performances are compared for the Sod shock tube problems. For the Sod problem without condensation, the speedup over an Intel CPU E7300 is 23 for the branch scheme and 41 for the overlapping scheme, respectively. While for problems with condensation, both schemes achieve higher acceleration ratios, 53 and 71, respectively. The higher speedup of the condensation case can be ascribed to the source term calculation which has a local dependence on the mesh point and the SOURCE kernel has a higher acceleration ratio.     

Local electronic and electrical properties of functionalized graphene nano flakes

Based on experimental findings models of amorphous graphene related carbon materials were generated using graphene nano flakes. On the optimized structures detailed local electronic properties were investigated using density functional theory. The electrical conductivities of all these models were also estimated using an in-house program based on tight-binding method. The calculated electrical conductivity values of all the models agreed well with the trend of calculated energy gap and graphitic character.     

Full potential calculation of electronic properties of rutile RO2 (R=Si, Ge, Sn and Pb) compounds via modified Becke Johnson potential

The electronic properties of RO₂ (R=Si, Ge, Sn and Pb; a group IVA element) compounds in rutile structure have been calculated using WIEN2k implementation of full potential linearized augmented plane wave (FPLAPW) method. The exchange and correlation (XC) effects are taken into account by an orbital independent modified Becke Johnson (MBJ) potential as coupled with Local Density Approximation (LDA) for all the compounds except for PbO₂ where only Generalized Gradient Approximation (GGA) is considered for the same. We predict a direct band gap in all these compounds with continuous decrease as the atomic size of IVA element increases such that there is an appearance of semimetallic band structure for the last compound, PbO₂. The largest band gap (7.66 eV) has been found for SiO₂, which governs its insulating nature. We observe that MBJLDA results for band gaps of these compounds are far better than those obtained using GGA and Engel-Vosko's GGA (EV-GGA). A very good agreement is observed between MBJLDA band gaps with corresponding experimental values as compared to other calculations. The electronic band structures are also analyzed in terms of contributions from various electrons.     

计算机控制光学表面成形中大规模驻留时间求解

采用基于稀疏矩阵的大规模非负最小二乘法,对大口径、微浮雕结构光学元件加工中的驻留时间进行了分析与求解,并对该算法开展了正则化研究。仿真结果表明:与传统非负最小二乘法相比,基于稀疏矩阵的大规模非负最小二乘法精度高、效率快。采用该算法仿真加工平均振幅为1.177 6倍波长的大口径、微浮雕结构光学元件,误差面形均方根收敛至0.067倍波长。     

冲击作用下HMX晶体孔洞塌缩热点生成机制的细观数值模拟

热点的形成、点火以及成长过程是理解非均匀炸药冲击起爆的关键.采用离散元法,对冲击作用下含孔洞的HMX晶体进行了细观数值模拟.计算结果表明:在较低冲击作用下,孔洞边缘发生了较大的剪切变形,粘塑性功形成热点;而在较高冲击作用下,孔洞塌缩产生射流,汇聚流动,冲击下游炸药形成热点,并获得了孔洞塌缩和热点生成演化的细观过程.