High-order curvilinear mesh generation technique based on an improved radius basic function approach

A high-order curvilinear hybrid mesh generation technique is developed for high-order numerical method (eg, discontinuous Galerkin method) applications to improve the accuracy for problems with curve boundary. The grid generation technique is based on an improved radius basic function (RBF) approach by which the straight-edge mesh is converted into high-order curve mesh. Firstly, an initial straight-edge mesh is prepared by traditional grid generation software. Then, high-order interpolation points are inserted into the mesh entities such as edges, faces, and cells according to the final demand of mesh order. To preserve the original geometry, the inserted points on solid wall are then projected onto the CAD model using an open source tool “Open Cascade.” Finally, other inserted points in the field near the solid wall are moved to appropriate positions by the improved RBF approach to avoid tangled cells. If we use the original RBF approach, then the inserted points on the edge and face entities normal to the solid boundary in the region of boundary layer will move to improper positions. To overcome this problem, a weighting based on the local grid aspect ratio between normal direction and tangential direction is introduced into the baseline RBF approach. Three typical configurations are tested to validate the mesh generator. Meanwhile, a third-order solution of subsonic flow over an analytical 3D body of revolution in the second International Workshop on High-Order CFD Methods is supplied by a discontinuous Galerkin solver. These numerical tests demonstrate the potential capability of present technique for high-order simulations of complex geometries.     

A matrix-free high-order discontinuous Galerkin compressible Navier-Stokes solver: A performance comparison of compressible and incompressible formulations for turbulent incompressible flows

Both compressible and incompressible Navier-Stokes solvers can be used and are used to solve incompressible turbulent flow problems. In the compressible case, the Mach number is then considered as a solver parameter that is set to a small value, M ≈0.1, in order to mimic incompressible flows. This strategy is widely used for high-order discontinuous Galerkin (DG) discretizations of the compressible Navier-Stokes equations. The present work raises the question regarding the computational efficiency of compressible DG solvers as compared to an incompressible formulation. Our contributions to the state of the art are twofold: Firstly, we present a high-performance DG solver for the compressible Navier-Stokes equations based on a highly efficient matrix-free implementation that targets modern cache-based multicore architectures with Flop/Byte ratios significantly larger than 1. The performance results presented in this work focus on the node-level performance, and our results suggest that there is great potential for further performance improvements for current state-of-the-art DG implementations of the compressible Navier-Stokes equations. Secondly, this compressible Navier-Stokes solver is put into perspective by comparing it to an incompressible DG solver that uses the same matrix-free implementation. We discuss algorithmic differences between both solution strategies and present an in-depth numerical investigation of the performance. The considered benchmark test cases are the three-dimensional Taylor-Green vortex problem as a representative of transitional flows and the turbulent channel flow problem as a representative of wall-bounded turbulent flows. The results indicate a clear performance advantage of the incompressible formulation over the compressible one.     

A Runge-Kutta–based WENO reconstruction on moving mesh for compressible fluids

In this paper, we construct a high-order moving mesh method based on total variation diminishing Runge-Kutta and weighted essential nonoscillatory reconstruction for compressible fluid system. Beginning with the integral form of fluid system, we get the semidiscrete system with an arbitrary mesh velocity. We use weighted essential nonoscillatory reconstruction to get the space accuracy on moving meshes, and the time accuracy is obtained by modified Runge-Kutta method; the mesh velocity is determined by moving mesh method. One- and two-dimensional numerical examples are presented to demonstrate the efficient and accurate performance of the scheme.     

A framework to perform high-order deconvolution for finite-volume method on simplicial meshes

In this article, a new framework to design high-order approximations in the context of node-centered finite volumes on simplicial meshes is proposed. The major novelty of this method is that it relies on very simple and compact differential operators, which is a critical point to achieve good performances in the High-performance computing context. This method is based on deconvolution between nodal and volume-average values, which can be conducted to any order. The interest of the new method is illustrated through three different applications: mesh-to-mesh interpolation, levelset curvature computation, and numerical scheme for convection. Higher order can also be achieved within the present framework by introducing high-rank tensors. Although these tensors feature much symmetries, their manipulation can quickly become an overwhelming task. For this reason and without loss of generality, the present articles are limited to third-order expansion. This method, although tightly connected to the k-exact schemes theory, does not rely on successive corrections: the high-order property is obtained in a single operation, which makes them more attractive in terms of performances.     

不均匀场中氢分子离子高次谐波产生的理论研究

在非Born-Oppenheimer近似下,通过求解含时薛定谔方程的方法,对氢分子离子在不均匀场中高次谐波的产生进行了理论研究.计算结果显示,同均匀场相比,电离的电子在不均匀场中加速会获得更多的能量,从而更有利于得到宽频谱.此外,通过优化不均匀场中的空间不均匀度,长量子路径被明显的抑制,最终通过叠加110阶到150阶谐波,获得一个60as的孤立阿秒脉冲.同时,通过库仑势和激光场的相互作用势以及时频分布图解释了其中的物理机制.     

Control of soliton characteristics of the condensate by an arbitrary x-dependent external potential

This paper presents a family of soliton solutions of the one-dimensional nonlinear Schrdinger equation which describes the dynamics of the dark solitons in Bose-Einstein condensates with an arbitrary x-dependent external potential.The obtained results show that the external potential has an important effect on the dark soliton dynamical characteristics of the condensates.The amplitude,width,and velocity of the output soliton are relative to the source position of the external potential.The smaller the amplitude of the soliton is,the narrower its width is,and the slower the soliton propagates.The collision of two dark solitons is nearly elastic.     

Metastable state and macroscopic quantum tunneling of binary mixtures

We provide a mixing model to explore the metastable state and the macroscopic quantum tunneling (MQT) of binary mixtures. For , we first observe the two condensates form the symmetry-breaking state (SBS) and then suddenly transfer to the symmetry-preserving state (SPS) through the MQT. The SBS is shown to be the metastable state in our system. We find the MQT does not spontaneously arise. The inducement mechanism is the damping but not the excitations. The damping mechanism can also control the lifetime and the tunneling decay rate of the SBS. Finally, we further present the origin of these phenomena by examining the energy of the system.     

Controlling the motion of solitons in BEC by a weakly periodic potential

By developing multiple-scale method combined with Wentzel--Kramer--Brillouin expansion, this paper analytically studies the modulating effect of weakly periodic potential on the dynamical properties of the Bose--Einstein condensates (BEC) trapped in harmonic magnetic traps. A black--grey soliton transition is observed in the BEC trapped in harmonic magnetic potential, due to the weakly periodic potential modulating effect. Meanwhile, it finds that with the slight increase of the weakly periodic potential strength, the velocity of the soliton decreases, while its width firstly decreases then increases, a minimum exists there. These results show that the amplitude, velocity, and width of matter solitons can be effectively managed by means of a weakly periodic potential.     

Quadrupolar matter-wave soliton in two-dimensional free space

We study two-dimensional (2D) matter-wave solitons in the mean-field models formed by electric quadrupole particles with long-range quadrupole–quadrupole interaction (QQI) in 2D free space. The existence of 2D matter-wave solitons in the free space was predicted using the 2D Gross–Pitaevskii Equation (GPE). We find that the QQI solitons have a higher mass (smaller size and higher intensity) and stronger anisotropy than the dipole–dipole interaction (DDI) solitons under the same environmental parameters. Anisotropic soliton–soliton interaction between two identical QQI solitons in 2D free space is studied. Moreover, stable anisotropic dipole solitons are observed, to our knowledge, for the first time in 2D free space under anisotropic nonlocal cubic nonlinearity.     

Role of excited states in the elliptically polarized harmonic generation

We theoretically investigate the contribution of the excited state to the ellipticity of the harmonics from H＋ at different orientation angles irradiated by a linearly polarized laser pulse. It is found that the first excited state has a significant influence to the ellipticity of the harmonics, and the contribution of higher excited states to the ellipticity can be neglected. Moreover, the conclusion is not dependent on the laser intensity.