A direct Eulerian GRP scheme for relativistic hydrodynamics: One-dimensional case

The paper proposes a direct Eulerian generalized Riemann problem (GRP) scheme for one-dimensional relativistic hydrodynamics. It is an extension of the Eulerian GRP scheme for compressible non-relativistic hydrodynamics proposed in [M. Ben-Artzi, J.Q. Li, G. Warnecke, A direct Eulerian GRP scheme for compressible fluid flows, J. Comput. Phys. 218 (2006) 19–43]. Two main ingredients, the Riemann invariant and the Rankine–Hugoniot jump condition, are directly used to resolve the local GRP in the Eulerian formulation, and thus the crucial and delicate Lagrangian treatment in the original GRP scheme [3] can be avoided. Several numerical examples are given to demonstrate the accuracy and effectiveness of the proposed GRP scheme.     

On the linearized relativistic Boltzmann equation. II. Existence of hydrodynamics

Solutions are analyzed of the linearized relativistic Boltzmann equation for initial data fromL ²(r, p) in long-time and/or small-mean-free-path limits. In both limits solutions of this equation converge to approximate ones constructed with solutions of the set of differential equations called the equations of relativistic hydrodynamics.     

Relativistic distribution function for particles with spin at local thermodynamical equilibrium

We present an extension of relativistic single-particle distribution function for weakly interacting particles at local thermodynamical equilibrium including spin degrees of freedom, for massive spin 1/2 particles. We infer, on the basis of the global equilibrium case, that at local thermodynamical equilibrium particles acquire a net polarization proportional to the vorticity of the inverse temperature four-vector field. The obtained formula for polarization also implies that a steady gradient of temperature entails a polarization orthogonal to particle momentum. The single-particle distribution function in momentum space extends the so-called Cooper–Frye formula to particles with spin 1/2 and allows us to predict their polarization in relativistic heavy ion collisions at the freeze-out.     

Kinetic theory based lattice Boltzmann equation with viscous dissipation and pressure work for axisymmetric thermal flows

A lattice Boltzmann equation (LBE) for axisymmetric thermal flows is proposed. The model is derived from the kinetic theory which exhibits several features that distinguish it from other previous LBE models. First, the present thermal LBE model is derived from the continuous Boltzmann equation, which has a solid foundation and clear physical significance; Second, the model can recover the energy equation with the viscous dissipation term and work of pressure which are usually ignored by traditional methods and the existing thermal LBE models; Finally, unlike the existing thermal LBE models, no velocity and temperature gradients appear in the force terms which are easy to realize in the present model. The model is validated by thermal flow in a pipe, thermal buoyancy-driven flow, and swirling flow in vertical cylinder by rotating the top and bottom walls. It is found that the numerical results agreed excellently with analytical solution or other numerical results.     

A relativistic quark model for mesons with an instanton-induced interaction

We present new results of a relativistic quark model based on the Bethe-Salpeter equation in its instantaneous approximation. Assuming a linearly rising confinement potential with an appropriate spinorial structure in Dirac space and adopting a residual interaction based on instanton effects, we can compute masses of the light mesons up to highest observed angular momenta with a natural solution of the U _A(1) problem. The calculated ground states masses and the radial excitations describe the experimental results well. In this paper, we will also discuss our results concerning numerous meson decay properties. For processes like π⁺/K ⁺↦e ⁺υ_eγ and 0^-↦γγ at various photon virtualities, we find a good agreement with experimental data. We will also comment on the form factors of the K _?3 decay and on the decay constants of the π, K and η mesons. For the sake of completeness, we will furthermore present the electromagnetic form factors of the charged π and K mesons as well as a comparison of the radiative meson decay widths with the most recent experimental data. Received: 28 August 2000 / Accepted: 12 September 2000     

A hybrid numerical method for interfacial fluid flow with soluble surfactant

We address a significant difficulty in the numerical computation of fluid interfaces with soluble surfactant that occurs in the physically representative limit of large bulk Peclet number Pe. At the high values of Pe in typical fluid-surfactant systems, there is a transition layer near the interface in which the surfactant concentration varies rapidly, and large gradients at the interface must be resolved accurately to evaluate the exchange of surfactant between the interface and bulk flow. We use the slenderness of the layer to develop a fast and accurate ‘hybrid’ numerical method that incorporates a separate, singular perturbation analysis of the dynamics in the transition layer into a full numerical solution of the interfacial free boundary problem. The accuracy and efficiency of the method is assessed by comparison with a more ‘traditional’ numerical approach that uses finite differences on a curvilinear coordinate system exterior to the bubble, without the separate transition layer reduction. The traditional method implemented here features a novel fast calculation of fluid velocity off the interface.     

A numerical scheme for the Stefan problem on adaptive Cartesian grids with supralinear convergence rate

We present a level set approach to the numerical simulation of the Stefan problem on non-graded adaptive Cartesian grids, i.e. grids for which the size ratio between adjacent cells is not constrained. We use the quadtree data structure to discretize the computational domain and a simple recursive algorithm to automatically generate the adaptive grids. We use the level set method on quadtree of Min and Gibou [C. Min, F. Gibou, A second order accurate level set method on non-graded adaptive Cartesian grids, J. Comput. Phys. 225 (2007) 300–321] to keep track of the moving front between the two phases, and the finite difference scheme of Chen et al. [H. Chen, C. Min, F. Gibou, A supra-convergent finite difference scheme for the poisson and heat equations on irregular domains and non-graded adaptive Cartesian grids, J. Sci. Comput. 31 (2007) 19–60] to solve the heat equations in each of the phases, with Dirichlet boundary conditions imposed on the interface. This scheme produces solutions that converge supralinearly (∼1.5)$(\sim 1.5)$ in both the L¹$L^1$ and the L^∞$L^{\infty }$ norms, which we demonstrate numerically for both the temperature field and the interface location. Numerical results also indicate that our method can simulate physical effects such as surface tension and crystalline anisotropy. We also present numerical data to quantify the saving in computational resources.     

A class of finite difference schemes with low dispersion and controllable dissipation for DNS of compressible turbulence

In this paper, a class of finite difference schemes which achieves low dispersion and controllable dissipation in smooth region and robust shock-capturing capabilities in the vicinity of discontinuities is presented. Firstly, a sufficient condition for semi-discrete finite difference schemes to have independent dispersion and dissipation is derived. This condition enables a novel approach to separately optimize the dissipation and dispersion properties of finite difference schemes and a class of schemes with minimized dispersion and controllable dissipation is thus obtained. Secondly, for the purpose of shock-capturing, one of these schemes is used as the linear part of the WENO scheme with symmetrical stencils to constructed an improved WENO scheme. At last, the improved WENO scheme is blended with its linear counterpart to form a new hybrid scheme for practical applications. The proposed scheme is accurate, flexible and robust. The accuracy and resolution of the proposed scheme are tested by the solutions of several benchmark test cases. The performance of this scheme is further demonstrated by its application in the direct numerical simulation of compressible turbulent channel flow between isothermal walls.     

用于脉冲等离子体推力器烧蚀过程仿真的新型机电模型

用于脉冲等离子体推力器(PPT)工作过程仿真的一维机电模型, 具有模型简单、计算周期短等优点, 在PPT设计过程中得到了广泛应用. 本文针对机电模型假设工质烧蚀质量为常数和不考虑烧蚀过程这一局限, 提出了一种采用Teflon一维烧蚀模型计算工质烧蚀质量的改进模型, 并以LES-6 PPT为研究对象进行了仿真. 通过与LES-6 PPT实验数据进行对比, 仿真结果与实验数据符合, 充分验证了模型的可靠性. 此模型能够对Teflon工质在PPT工作过程中的温度变化和烧蚀过程进行仿真, 弥补了机电模型忽略烧蚀过程对仿真结果所造成的影响, 同时, 此模型依然保持了机电模型简单易于实现的优点, 对于脉冲等离子体推力器的设计具有重要意义. 关键词： 脉冲等离子体推力器 机电模型 烧蚀模型 数值仿真     

A high-order cut-cell method for numerical simulation of hypersonic boundary-layer instability with surface roughness

Laminar-turbulent transition of hypersonic boundary layers can be affected significantly by the existence of surface roughness. Currently many important mechanisms of roughness-induced transition are not well understood. In recent years, direct numerical simulation (DNS) has been extensively applied for investigating instability and transition mechanisms of hypersonic boundary layers. Most of the past DNS studies, however, have been based on body-fitted grids for smooth surfaces without roughness. Due to complex geometry of embedded roughness, the use of body-fitted grids can be very difficult for flow with arbitrary surface roughness. In this paper, we present a new high-order cut-cell method to overcome the natural complexities in grid generation around arbitrary surface of roughness. The new method combines a non-uniform-grid finite-difference method for discrete grid points near the solid boundary and a shock-fitting method for the treatment of the bow shock. The non-uniform-grid finite-difference formulas are expressed in a general explicit form so that they can be applied to different multi-dimensional problems without any modification. The computational accuracy of new algorithms of up to O(h⁴) are tested on several one- and two-dimensional elliptic equations in irregular domains. In addition, the new method is applied to the simulation of the receptivity process of a Mach 5.92 flow over a flat plate under the combined effect of an isolated surface roughness element and surface blow and suction. A good agreement is found between the unsteady flow results and those obtained by a Linear Stability Theory (LST).     

A scheme for recording a fast process at nanosecond scale by using digital holographic interferometry with continuous wave laser

A scheme for recording fast process at nanosecond scale by using digital holographic interferometry with continuous wave (CW) laser is described and demonstrated experimentally, which employs delayed-time fibers and angular multiplexing technique and can realize the variable temporal resolution at nanosecond scale and different measured depths of object field at certain temporal resolution. The actual delay-time is controlled by two delayed-time fibers with different lengths. The object field information in two different states can be simultaneously recorded in a composite hologram. This scheme is also suitable for recording fast process at picosecond scale, by using an electro-optic modulator.     

A numerical scheme for the solution of axisymmetric radiative transfer problems in irregular domains filled by media with opaque and transparent diffuse and specular boundaries

This paper presents a new numerical scheme of the discrete ordinates method for the solution of axisymmetric radiative transfer problems in irregular domains filled by media with opaque and transparent diffuse and specular (Fresnel) boundaries and interfaces. New test problems of radiative transfer, which describe radiative transfer in domains with Fresnel interfaces, are proposed in this paper. These problems admit analytic solutions and can be used as benchmark ones. The proposed scheme is applied to the solution of the problems. Numerical results show that the presence of Fresnel interfaces leads to an appreciably larger error in numerical solution. This is connected with the “discontinuity” of the Fresnel reflectivity, which, through numerical diffusion, leads to the distortion of numerical solution. Modification of the scheme allows to reduce the numerical error.     

A method for calculating the surface tension of a droplet in a lattice-gas model with long-range interaction

Since the droplet of the lattice-gas model with long-range interaction is not circular and is determined by the Wulff construction due to surface tension anisotropy, a calculation method of the surface tension of the droplet is proposed in this paper. The calculated surface tension is in good agreement with the surface tension measured by using the Laplace's formula in consideration of the surface thickness. Received 15 March 2000 and Received in final form 31 May 2000