An adaptive SPH method for strong shocks

We propose an alternative SPH scheme to usual SPH Godunov-type methods for simulating supersonic compressible flows with sharp discontinuities. The method relies on an adaptive density kernel estimation (ADKE) algorithm, which allows the width of the kernel interpolant to vary locally in space and time so that the minimum necessary smoothing is applied in regions of low density. We have performed a von Neumann stability analysis of the SPH equations for an ideal gas and derived the corresponding dispersion relation in terms of the local width of the kernel. Solution of the dispersion relation in the short wavelength limit shows that stability is achieved for a wide range of the ADKE parameters. Application of the method to high Mach number shocks confirms the predictions of the linear analysis. Examples of the resolving power of the method are given for a set of difficult problems, involving the collision of two strong shocks, the strong shock-tube test, and the interaction of two blast waves.     

An all-speed relaxation scheme for interface flows with surface tension

We consider interface flows where compressibility and capillary forces (surface tension) are significant. These flows are described by a non-conservative, unconditionally hyperbolic multiphase model. The numerical approximation is based on finite-volume method for unstructured grids. At the discrete level, the surface tension is approximated by a volume force (CSF formulation). The interface physical properties are recovered by designing an appropriate linearized Riemann solver (Relaxation scheme) that prevents spurious oscillations near material interfaces. For low-speed flows, a preconditioning linearization is proposed and the low Mach asymptotic is formally recovered. Numerical computations, for a bubble equilibrium, converge to the required Laplace law and the dynamic of a drop, falling under gravity, is in agreement with experimental observations.     

A semi-coherent interface with nanoledges intersecting the free surface of an elastic half-space

Abstract

The elastic field generated by a semi-coherent interface formed by a succession of parallel terraces and nanoledges is investigated when the interface intersects the free surface of an isotropic half-space medium. The method uses the combination of semi-infinite Somigliana dislocations placed on each terrace and semi-infinite translation (or Volterra) dislocations placed at one or two corners of the nanoledges. Numerical examples depict the deformation fields nearby emerging regions of two semi-coherent interfaces; one is flat, while the other includes nanoledges.     

An interface capturing method for the simulation of multi-phase compressible flows

A novel finite-volume interface (contact) capturing method is presented for simulation of multi-component compressible flows with high density ratios and strong shocks. In addition, the materials on the two sides of interfaces can have significantly different equations of state. Material boundaries are identified through an interface function, which is solved in concert with the governing equations on the same mesh. For long simulations, the method relies on an interface compression technique that constrains the thickness of the diffused interface to a few grid cells throughout the simulation. This is done in the spirit of shock-capturing schemes, for which numerical dissipation effectively preserves a sharp but mesh-representable shock profile. For contact capturing, the formulation is modified so that interface representations remain sharp like captured shocks, countering their tendency to diffuse via the same numerical diffusion needed for shock-capturing. Special techniques for accurate and robust computation of interface normals and derivatives of the interface function are developed. The interface compression method is coupled to a shock-capturing compressible flow solver in a way that avoids the spurious oscillations that typically develop at material boundaries. Convergence to weak solutions of the governing equations is proved for the new contact capturing approach. Comparisons with exact Riemann problems for model one-dimensional multi-material flows show that the interface compression technique is accurate. The method employs Cartesian product stencils and, therefore, there is no inherent obstacles in multiple dimensions. Examples of two- and three-dimensional flows are also presented, including a demonstration with significantly disparate equations of state: a shock induced collapse of three-dimensional van der Waal’s bubbles (air) in a stiffened equation of state liquid (water) adjacent to a Mie-Grüneisen equation of state wall (copper).     

The potential energy surface and chaos in 2D Hamiltonian systems

We provide a new insight into the relationship between the geometric property of the potential energy surface and chaotic behavior of 2D Hamiltonian dynamical systems, and give an indicator of chaos based on the geometric property of the potential energy surface by defining Mean Convex Index (MCI). We also discuss a model of unstable Hamiltonian in detail, and show our results in good agreement with HBLSL's (Horwitz, Ben Zion, Lewkowicz, Schiffer and Levitan) new Riemannian geometric criterion.     

An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries

We present an immersed interface method for solving the incompressible steady Stokes equations involving fixed/moving interfaces and rigid boundaries (irregular domains). The fixed/moving interfaces and rigid boundaries are represented by a number of Lagrangian control points. In order to enforce the prescribed velocity at the rigid boundaries, singular forces are applied on the fluid at these boundaries. The strength of singular forces at the rigid boundary is determined by solving a small system of equations. For the deformable interfaces, the forces that the interface exerts on the fluid are calculated from the configuration (position) of the deformed interface. The jumps in the pressure and the jumps in the derivatives of both pressure and velocity are related to the forces at the fixed/moving interfaces and rigid boundaries. These forces are interpolated using cubic splines and applied to the fluid through the jump conditions. The positions of the deformable interfaces are updated implicitly using a quasi-Newton method (BFGS) within each time step. In the proposed method, the Stokes equations are discretized via the finite difference method on a staggered Cartesian grid with the incorporation of jump contributions and solved by the conjugate gradient Uzawa-type method. Numerical results demonstrate the accuracy and ability of the proposed method to simulate incompressible Stokes flows with fixed/moving interfaces on irregular domains.     

Edge misfit dislocation formation at the interface of a nanopore and infinite substrate with surface/interface effects

The model of an edge misfit dislocation at the interface of the hollow nanopore and the infinite substrate with surface/interface stress is investigated. Using the complex variable method, analytical solutions for complex potentials of a film due to an edge misfit dislocation located in the film with surface/interface effect are derived, and the stress fields of the film and the edge misfit dislocation formation energy can be obtained. The critical conditions for edge misfit dislocation formation are given at which the generation of an edge misfit dislocation is energetically favourable. The influence of the ratio of the shear modulus between the film and the infinite substrate, the misfit strain, the radius of the nanopore and the surface/interface stress on the critical thickness of the film is discussed.     

An energy-consistency-preserving large eddy simulation-scalar filtered mass density function (LES-SFMDF) method for high-speed flows

An energy-consistency-preserving large eddy simulation-scalar filtered mass density function (LES-SFMDF) method is developed to improve the existing LES-SFMDF method in high-speed flows, especially supersonic flows. The high-speed source term in the SFMDF transport equation is analysed theoretically from a new point of view, and then several primary principles are proposed for the LES-SFMDF to achieve a good consistency even along discontinuities. Based on these principles and further theoretical analysis, the high-speed source term of the enthalpy in the SFMDF is modelled and computed from both MC and LES variables rather than the usually used solely LES variables. This new LES-SFMDF method is used for simulating the flows in a shock tube and in a subsonic temporally developing mixing layer. This method shows a better particle energy consistency than the existing method when applied across discontinuities in supersonic laminar flows. Unlike the existing method, with this energy-consistency-preserving LES-SFMDF method, particle energy consistency is consistent with particle mass consistency so that particle energy consistency can benefit from particle velocity correction. This method also demonstrates robustness for various numbers of particles.     

Stability analysis on the free surface phenomena of a magnetic fluid for general use

This paper presents an analysis for elucidating a variety of physical processes on the interface (free surface) of magnetic fluid. The present analysis is composed of the magnetic and the fluid analysis, both of which have no limitations concerning the interface elevation or its profile. The magnetic analysis provides rigorous interface magnetic field under arbitrary distributions of applied magnetic field. For the fluid analysis, the equation for interface motion includes all nonlinear effects. Physical quantities such as the interface magnetic field or the interface stresses, obtained first as the wavenumber components, facilitate confirming the relations with those by the conventional theoretical analyses. The nonlinear effect is formulated as the nonlinear mode coupling between the interface profile and the applied magnetic field. The stability of the horizontal interface profile is investigated by the dispersion relation, and summarized as the branch line. Furthermore, the balance among the spectral components of the interface stresses are shown, within the sufficient range of the wavenumber space.     

Laser photochromic dye activation technique for the measurement of liquid free surface velocity on curved surfaces

An optical method is presented which permits the determination of the free surface velocity of liquid films flowing on curved surfaces. The feasibility of this technique, which involves the laser tomography and photochromic dye activation techniques, is demonstrated on an oil film flowing around a finned tube. Results for different tube geometries and flow conditions are presented. Advantages and limits of the laser photochromic velocimetry technique are discussed.     

液滴在气固交界面变形移动问题的光滑粒子流体动力学模拟

为准确模拟液滴在气固交界面变形移动问题,对基于连续表面张力模型的表面张力光滑粒子流体动力学方法进行了改进.改进方法采用新的边界处理方式和界面法向修正方法,即将固体边界虚粒子色函数值根据液面的位置进行相应设定以保证气-液-固三相交界处流体粒子的界面法向沿接触线法线方向,引入Brackbill提出的壁面附着力边界条件处理方法,对在气-液-固三相交界处的流体粒子及部分固体边界虚粒子的界面法向进行修正,修正前后保持法向模值不变,得到了含壁面附着力边界条件的表面张力算法.模拟了受壁面附着力影响的水槽中液面的变化过程、液滴润湿壁面过程和剪切气流驱动液滴在固体表面变形脱落过程,并与流体体积函数方法进行了对比.结果表明,该方法在处理壁面附着力问题时精度较高,稳定性较好,适合处理工程中液滴在气固交界面变形移动问题.     

Linking anisotropic sharp and diffuse surface motion laws via gradient flows

We compare four surface motion laws for sharp surfaces with their diffuse interface counterparts by means of gradient flows on corresponding energy functionals. The energy functionals can be defined to give the same dependence on normal direction for the energy of sharp plane surfaces as for their diffuse counterparts. The anisotropy of the kinetics can be incorporated into the inner product without affecting the energy functional.     

Metal CVD for microelectronic applications: An examination of surface chemistry and kinetics

We review the surface chemistry and kinetics relevant to the chemical vapor deposition (CVD) of metals used for microelectronic applications. Our efforts focus on the surface chemistry of aluminum, tungsten, and copper CVD, which have received the most recent interest for metallization. We first briefly review a variety of topics concerning the applications and the chemistry and kinetics of metal CVD. We also give a brief overview of the application of surface science techniques to the study of CVD-related surface chemistry.     

A millimeter and sub-millimeter wave frequency selective surface beamsplitter for geostationary orbit microwave radiometers

We report the design of three frequency selective surface(FSS) filters used on the FengYun-4(FY-4) microwave satellite,which separate five-frequency bands in the frequency range of 50-429 GHz with the insertion loss less than 0.4 dB,and separation between adjacent channels more than 20 dB for either TE or TM incidence.Firstly,we briefly introduce the disadvantages of two types of FSS filter:waveguide-array FSS and printed FSS,which are commonly employed in the millimeter and sub-millimeter wave band.In order to meet the insertion loss requirement and specified spectral transmission response,we adopt a filter composed of two closely spaced freestanding metal plates,which contains an array of resonant ring slot elements.Computer simulation technology(CST) is used to optimize the structural dimensions of the resonant unit and interlayer separation.Numerical results show that these FSS filters exhibit transmission loss of less than 0.4 dB and separation between adjacent channels of more than 20 dB.Simulated transmission coefficients are in close agreement with the required specification,and even exceed the performance specifications.     

An ammonium sulfate/ethanol aqueous two-phase system combined with ultrasonication for the separation and purification of lithospermic acid B from Salvia miltiorrhiza Bunge

We studied the effect of ultrasonication extraction technology combined with ammonium sulfate/ethanol aqueous two-phase system (ATPS) for the separation of lithospermic acid B (LAB) from Salvia miltiorrhiza Bunge. According to the literature and preliminary studies, ammonium sulfate concentration, ethanol concentration, pH, ultrasonication power, ultrasonication time and the ratio of solvent-to-solid were investigated using a single factor design to identify the factors affecting separation. Taking into consideration a simultaneous increase in LAB recovery (R (%)) and partition coefficient (K), the best performance of the ATPS was obtained at 25 °C and pH 2 using ammonium sulfate 22% (w/w) and ethanol 30% (w/w). To keep the solvent-to-solid ratio at 10, response surface methodology was used to find the optimal ultrasonication power and ultrasonication time. Quadratic models were predicted for LAB yield in the upper phase. Optimal conditions of 572.1 W ultrasonication power and 42.2 min produced a maximum yield of LAB of 42.16 mg g⁻¹ sample. There was no obvious degradation of LAB with ultrasound under the applied conditions, and the experimental yield of LAB was 42.49 mg g⁻¹ sample and the purity was 55.28% (w/w), which was much higher than that obtained using conventional extraction. The present study demonstrated that ultrasound coupled with aqueous two-phase systems is very efficient tool for the extraction and purification of LAB from Salvia miltiorrhiza Bunge.