Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second order discretization using a Total Variation Diminishing (TVD) scheme for the terms representing advection of the distribution function in physical space, due to microscopic particle motion. The advantage of the LBE approach is exploited by implementing the scheme in a new computer code to run on a parallel computing system. Performance of the new formulation is systematically investigated by simulating four benchmark flows of increasing complexity, namely (1) flow in a plane channel, (2) unsteady Couette flow, (3) flow caused by a moving lid over a 2D square cavity and (4) flow over a circular cylinder. For each of these flows, the present scheme is validated with the results from Navier–Stokes computations as well as lattice Boltzmann simulations on regular mesh. It is shown that the scheme is robust and accurate for the different test problems studied.     

An unconditionally stable fully conservative semi-Lagrangian method

Semi-Lagrangian methods have been around for some time, dating back at least to [3]. Researchers have worked to increase their accuracy, and these schemes have gained newfound interest with the recent widespread use of adaptive grids where the CFL-based time step restriction of the smallest cell can be overwhelming. Since these schemes are based on characteristic tracing and interpolation, they do not readily lend themselves to a fully conservative implementation. However, we propose a novel technique that applies a conservative limiter to the typical semi-Lagrangian interpolation step in order to guarantee that the amount of the conservative quantity does not increase during this advection. In addition, we propose a new second step that forward advects any of the conserved quantity that was not accounted for in the typical semi-Lagrangian advection. We show that this new scheme can be used to conserve both mass and momentum for incompressible flows. For incompressible flows, we further explore properly conserving kinetic energy during the advection step, but note that the divergence free projection results in a velocity field which is inconsistent with conservation of kinetic energy (even for inviscid flows where it should be conserved). For compressible flows, we rely on a recently proposed splitting technique that eliminates the acoustic CFL time step restriction via an incompressible-style pressure solve. Then our new method can be applied to conservatively advect mass, momentum and total energy in order to exactly conserve these quantities, and remove the remaining time step restriction based on fluid velocity that the original scheme still had.     

A novel coupled level set and volume of fluid method for sharp interface capturing on 3D tetrahedral grids

We present a new three-dimensional hybrid level set (LS) and volume of fluid (VOF) method for free surface flow simulations on tetrahedral grids. At each time step, we evolve both the level set function and the volume fraction. The level set function is evolved by solving the level set advection equation using a second-order characteristic based finite volume method. The volume fraction advection is performed using a bounded compressive normalized variable diagram (NVD) based scheme. The interface is reconstructed based on both the level set and the volume fraction information. The novelty of the method lies in that we use an analytic method for finding the intercepts on tetrahedral grids, which makes interface reconstruction efficient and conserves volume of fluid exactly. Furthermore, the advection of volume fraction makes use of the NVD concept and switches between different high resolution differencing schemes to yield a bounded scalar field, and to preserve both smoothness and sharp definition of the interface. The method is coupled to a well validated finite volume based Navier–Stokes incompressible flow solver. The code validation shows that our method can be employed to resolve complex interface changes efficiently and accurately. In addition, the centroid and intercept data available as a by-product of the proposed interface reconstruction scheme can be used directly in near-interface sub-grid models in large eddy simulation.     

Three-dimensional key in a modified joint transform correlator encryption scheme

We propose a modified encryption joint transform correlator scheme that introduces an additional random phase mask. The positions of both the conventional and the new mask are crucial for successful recovery of the original data. Although the two random phase masks are 2D, variation of their relative distance constitutes an additional dimension. Consequently by including this notion, both random phase masks act as a 3-dimensional (3D) key code increasing thereby the security with respect to the conventional JTC encryption scheme. We employ this scheme to multiplex encrypted data, displacing the encoding masks. During decryption of the multiplexed information, we only reconstruct the object that matches the correct predetermined 3D key code, i.e. that matches the random masks positions in the encryption step. We present actual experimental results, by using BSO crystal as recording medium, as well as their respective analysis.     

A robust numerical scheme for highly compressible magnetohydrodynamics: Nonlinear stability,implementation and tests

The ideal MHD equations are a central model in astrophysics, and their solution relies upon stable numerical schemes. We present an implementation of a new method, which possesses excellent stability properties. Numerical tests demonstrate that the theoretical stability properties are valid in practice with negligible compromises to accuracy. The result is a highly robust scheme with state-of-the-art efficiency. The scheme’s robustness is due to entropy stability, positivity and properly discretised Powell terms. The implementation takes the form of a modification of the MHD module in the FLASH code, an adaptive mesh refinement code. We compare the new scheme with the standard FLASH implementation for MHD. Results show comparable accuracy to standard FLASH with the Roe solver, but highly improved efficiency and stability, particularly for high Mach number flows and low plasma β. The tests include 1D shock tubes, 2D instabilities and highly supersonic, 3D turbulence. We consider turbulent flows with RMS sonic Mach numbers up to 10, typical of gas flows in the interstellar medium. We investigate both strong initial magnetic fields and magnetic field amplification by the turbulent dynamo from extremely high plasma β. The energy spectra show a reasonable decrease in dissipation with grid refinement, and at a resolution of 512³ grid cells we identify a narrow inertial range with the expected power law scaling. The turbulent dynamo exhibits exponential growth of magnetic pressure, with the growth rate higher from solenoidal forcing than from compressive forcing. Two versions of the new scheme are presented, using relaxation-based 3-wave and 5-wave approximate Riemann solvers, respectively. The 5-wave solver is more accurate in some cases, and its computational cost is close to the 3-wave solver.     

A conservative scheme for the relativistic Vlasov–Maxwell system

A new scheme for numerical integration of the 1D2V relativistic Vlasov–Maxwell system is proposed. Assuming that all particles in a cell of the phase space move with the same velocity as that of the particle located at the center of the cell at the beginning of each time step, we successfully integrate the system with no artificial loss of particles. Furthermore, splitting the equations into advection and interaction parts, the method conserves the sum of the kinetic energy of particles and the electromagnetic energy. Three test problems, the gyration of particles, the Weibel instability, and the wakefield acceleration, are solved by using our scheme. We confirm that our scheme can reproduce analytical results of the problems. Though we deal with the 1D2V relativistic Vlasov–Maxwell system, our method can be applied to the 2D3V and 3D3V cases.     

A General-Purpose Finite-Volume Advection Scheme for Continuous and Discontinuous Fields on Unstructured Grids

We present a new general-purpose advection scheme for unstructured meshes based on the use of a variation of the interface-tracking flux formulation recently put forward by O. Ubbink and R. I. Issa (J. Comput. Phys.153, 26 (1999)), in combination with an extended version of the flux-limited advection scheme of J. Thuburn (J. Comput. Phys.123, 74 (1996)), for continuous fields. Thus, along with a high-order mode for continuous fields, the new scheme presented here includes optional integrated interface-tracking modes for discontinuous fields. In all modes, the method is conservative, monotonic, and compatible. It is also highly shape preserving. The scheme works on unstructured meshes composed of any kind of connectivity element, including triangular and quadrilateral elements in two dimensions and tetrahedral and hexahedral elements in three dimensions. The scheme is finite-volume based and is applicable to control-volume finite-element and edge-based node-centered computations. An explicit–implicit extension to the continuous-field scheme is provided only to allow for computations in which the local Courant number exceeds unity. The transition from the explicit mode to the implicit mode is performed locally and in a continuous fashion, providing a smooth hybrid explicit–implicit calculation. Results for a variety of test problems utilizing the continuous and discontinuous advection schemes are presented.     

水中障碍物爆炸毁伤效应的二维数值模拟

 建立了水下障碍物的爆炸毁伤效应的物理模型和计算模型。建立了守恒方程组、混凝土的动态弹塑性本构关系和破坏准则,并确定了其在大应变、高应变率及高压条件下的的屈服准则。基于多物质流体的Euler算法,用面向对象的C++语言自行编制了NM-MMIC通用多物质二维流体弹塑性程序,对不同炸点位置、不同炸药量对轨条砦爆炸破坏过程进行数值模拟,并采用自行开发的后处理软件VISC2D实现了可视化,定量地反应了障碍物迎爆面所承受的压力变化过程,确定了轨条砦毁伤的最佳药量,并对毁伤程度进行了评价,得到了爆炸破障的毁伤规律。研究结果对设计和评价反水中障碍物的弹药具有一定的参考价值。     

On the computation of sound in free and wall-bounded domains

A new Dispersion-Relation-Preserving (DRP) scheme has been developed using the Lax-Wendroff methodology. Two collocated grids are placed in a staggered formation and a staggered DRP scheme is used to calculate the spatial differentiation of the propagation and convection terms. A staggered filtering scheme of a six points stencil is developed to complete the transformation from one grid to another. Existing DRP Runge-Kutta schemes are used for the time marching. Stability limits and accuracy issues are investigated using a simple 1D advection equation. The new method is then tested for monopole and quadrupole radiation, diffraction effects of an aperture in a wall, and convection effects of shear flow. All demonstrate the good accuracy and numerical stability of the new method.     

基于非线性迭代的压水堆瞬态计算程序开发

采用目前工业上成熟的非线性迭代计算策略,基于两群粗网有限差分方法和多群UNM节块方法,开发了针对压水堆工况的三维瞬态扩散计算程序。UNM方法采用解析基函数作为基函数,通过方程变换解决了解析节块法在临界节块计算不稳定的问题,提高了计算精度。热工计算采用单通道模型和燃料棒一维导热模型,相比目前堆芯在用的经验关系式方法,该模型可以更加准确地计算燃料棒温度分布。采用基于横向积分方程的三节块方法,可以有效减轻控制棒尖齿效应对瞬态计算的影响。为测试程序性能,采用NEACRP等基准算例对程序进行了校验。数值结果表明,开发的程序计算结果正确,适用于压水堆堆芯瞬态过程的模拟。     

An improved particle correction procedure for the particle level set method

The particle level set method [D. Enright, R. Fedkiw, J. Ferziger, I. Mitchell, A hybrid particle level set method for improved interface capturing, J. Comput. Phys. 183 (2002) 83–116.] can substantially improve the mass conservation property of the level set method by using Lagrangian marker particles to correct the level set function in the under-resolved regions. In this study, the limitations of the particle level set method due to the errors introduced in the particle correction process are analyzed, and an improved particle correction procedure is developed based on a new interface reconstruction scheme. Moreover, the zero level set is “anchored” as the level set functions are reinitialized; hence the additional particle correction after the level set reinitialization is avoided. With this new scheme, a well-defined zero level set can be obtained and the disturbances to the interface are significantly reduced. Consequently, the particle reseeding operation will barely result in the loss of interface characteristics and can be applied as frequently as necessary. To demonstrate the accuracy and robustness of the proposed method, two extreme particle reseeding strategies, one without reseeding and the other with reseeding every time step, are applied in several benchmark advection tests and the results are compared with each other. Three interfacial flow cases, a 2D surface tension driven oscillating droplet, a 2D gas bubble rising in a quiescent liquid, and a 3D drop impact onto a liquid pool are simulated to illustrate the advantages of the current method over the level set and the original particle level set methods with regard to the smoothness of geometric properties and mass conservation in real physical applications.     

Shock-stable flux scheme for predicting aerodynamic heating load of hypersonic airliners

In the design of a hypersonic airliner that can considerably shorten the flight time, how to accurately predict the vehicle's aerodynamic heating loads is of great significance. In this study, a new shock-stable flux scheme called the simple low dissipation advection upwind splitting method(SLAU)-M1 is proposed for the prediction of hypersonic aerodynamic heating load. Based on the construction of the SLAU scheme for low-speed simulations, SLAU-M1 improves the robustness of the mass flux against shock instability. After validating the code employed, several numerical test cases are conducted. The onedimensional(1D) sod shock tube case and the two-dimensional(2D) inviscid NACA0012 airfoil case show that SLAU-M1 features a high level of accuracy at both low and high speeds. To simulate the hypersonic viscous flow over a blunt cone, we adopt different aspect ratios(ARs) of cells near the shock. The results suggest that SLAU-M1 is much less sensitive to the AR of cells near the shock in predicting hypersonic aerodynamic heating loads. Moreover, the findings show that the theoretical value is considerably better than that of the other schemes. The hypersonic viscous flow over a 2D double ellipsoid case and that over the Hypersonic Flight Experiment vehicle case also indicate that SLAU-M1 exhibits a considerably high level of accuracy in hypersonic heating predictions. These properties suggest that SLAU-M1 promises to be widely used in the accurate prediction of the aerodynamic heating loads of hypersonic airliners.     

A 6th order staggered compact finite difference method for the incompressible Navier–Stokes and scalar transport equations

In a previous paper we have developed a staggered compact finite difference method for the compressible Navier–Stokes equations. In this paper we will extend this method to the case of incompressible Navier–Stokes equations. In an incompressible flow conservation of mass is ensured by the well known pressure correction method  and . The advection and diffusion terms are discretized with 6th order spatial accuracy. The discrete Poisson equation, which has to be solved in the pressure correction step, has the same spatial accuracy as the advection and diffusion operators. The equations are integrated in time with a third order Adams–Bashforth method. Results are presented for a 1D advection–diffusion equation, a 2D lid driven cavity at a Reynolds number of 1000 and 10,000 and finally a 3D fully developed turbulent duct flow at a bulk Reynolds number of 5400. In all cases the methods show excellent agreement with analytical and other numerical and experimental work.     

水珠滴落的最小二乘粒子有限元方法模拟

提出了一种最小二乘粒子有限元方法,用其模拟了二维水珠滴落水面并飞溅散开的过程.该法基于拉格朗日描述,在每个时间步上使用扩展的Delaunay划分更新计算网格,并应用α形方法识别自由面形状;用最小二乘有限元方法离散流体运动的Navier-Stokes方程,并推导了一种自适应时间步长方案以提高计算效率和鲁棒性;引入网格拉伸技术修正减小流体质量误差.对水滴飞溅进行仿真,得到了与商用软件Flow-3d比较符合的结果,且具有更清晰锐利的自由面. 关键词： 滴落 网格划分 α形')" href="#">α形 最小二乘有限元     

Multiple Observations for Secret-Key Binding with SRAM PUFs

We present a new Multiple-Observations (MO) helper data scheme for secret-key binding to an SRAM-PUF. This MO scheme binds a single key to multiple enrollment observations of the SRAM-PUF. Performance is improved in comparison to classic schemes which generate helper data based on a single enrollment observation. The performance increase can be explained by the fact that the reliabilities of the different SRAM cells are modeled (implicitly) in the helper data. We prove that the scheme achieves secret-key capacity for any number of enrollment observations, and, therefore, it is optimal. We evaluate performance of the scheme using Monte Carlo simulations, where an off-the-shelf LDPC code is used to implement the linear error-correcting code. Another scheme that models the reliabilities of the SRAM cells is the so-called Soft-Decision (SD) helper data scheme. The SD scheme considers the one-probabilities of the SRAM cells as an input, which in practice are not observable. We present a new strategy for the SD scheme that considers the binary SRAM-PUF observations as an input instead and show that the new strategy is optimal and achieves the same reconstruction performance as the MO scheme. Finally, we present a variation on the MO helper data scheme that updates the helper data sequentially after each successful reconstruction of the key. As a result, the error-correcting performance of the scheme is improved over time.     

煤油超燃冲压发动机三维大规模并行数值模拟

在我国巨型计算机上,采用1024个CPU对煤油燃料超燃冲压发动机燃烧流场进行三维大规模并行数值模拟.计算软件采用自主研发的并行软件AHL3D,控制方程采用雷诺平均的N-S方程,无粘项计算采用Steger-Warning矢通量分裂格式,湍流模型采用k-ω双方程模型,煤油分子式采用正癸烷代替.计算给出的发动机壁面压强分布与试验测量结果有较好的一致性.结果表明,凹槽是发动机主要的着火区和火焰稳定区,同时,由于燃料的喷注形成的回流区也起到一定的稳焰作用.计算结果验证了AHL3D程序和采用的理论模型可以用于模拟煤油燃料超燃冲压发动机内部的复杂流动.     

用于太赫兹源粒子模拟的有限电导率模块研制

针对THz频段微电真空器件波导壁面材料电导率及加工粗糙度引发损耗的模拟需求,研制了有限电导率模块,并将其添加进三维全电磁粒子模拟大规模并行程序NEPTUNE3D。介绍了有限电导率的时域有限差分显格式及时谐场近似解方法,针对上述方法的优缺点,提出了基于扩散方程隐格式的有限电导率模块算法,该算法具备无条件稳定、普适性好的优点。利用矩波导常见电磁波模传输损耗算例,测试了自编的有限电导率模块,测试结果与理论值及同类商业电磁软件计算结果进行了比对,验证了模块的可靠性。利用添加有限电导率的三维全电磁粒子模拟程序NEPTUNE3D,模拟了材料电导率以及表面粗糙度对0.22 THz折叠波导行波管性能的影响,模拟结果表明,材料电导率及表面粗糙度会显著降低器件输出功率和增益水平。综合色散关系、耦合阻抗、衰减常数等因素,给出了器件结构参数设计建议,并指出:通过增加电子束流、注入信号功率以及慢波结构周期数目等方式可一定程度上提高器件输出功率水平。     

A fourth-order adaptive mesh refinement algorithm for the multicomponent,reacting compressible Navier–Stokes equations

In this paper, we present a fourth-order in space and time block-structured adaptive mesh refinement algorithm for the compressible multicomponent reacting Navier–Stokes equations. The algorithm uses a finite-volume approach that incorporates a fourth-order discretisation of the convective terms. The time-stepping algorithm is based on a multi-level spectral deferred corrections method that enables explicit treatment of advection and diffusion coupled with an implicit treatment of reactions. The temporal scheme is embedded in a block-structured adaptive mesh refinement algorithm that includes subcycling in time with spectral deferred correction sweeps applied on levels. Here we present the details of the multi-level scheme paying particular attention to the treatment of coarse–fine boundaries required to maintain fourth-order accuracy in time. We then demonstrate the convergence properties of the algorithm on several test cases including both non-reacting and reacting flows. Finally we present simulations of a vitiated dimethyl ether jet in 2D and a turbulent hydrogen jet in 3D, both with detailed kinetics and transport.     

Particle-in-cell simulations with charge-conserving current deposition on graphic processing units

We present an implementation of a 2D fully relativistic, electromagnetic particle-in-cell code, with charge-conserving current deposition, on parallel graphics processors (GPU) with CUDA. The GPU implementation achieved a one particle-step process time of 2.52 ns for cold plasma runs and 9.15 ns for extremely relativistic plasma runs, which are respectively 81 and 27 times faster than a single threaded state-of-art CPU code. A particle-based computation thread assignment was used in the current deposition scheme and write conflicts among the threads were resolved by a thread racing technique. A parallel particle sorting scheme was also developed and used. The implementation took advantage of fast on-chip shared memory, and can in principle be extended to 3D.     

A multistep flux-corrected transport scheme

A multistep flux-corrected transport (MFCT) scheme is developed to achieve conservative and monotonic tracer transports for multistep dynamical cores. MFCT extends Zalesak two-time level scheme to any multistep time-differencing schemes by including multiple high-order fluxes in the antidiffusive flux, while computing the two-time level low-order monotone solution. The multistep time-differencing scheme used in this study is the third-order Adams–Bashforth (AB3) scheme implemented in a finite-volume icosahedral shallow-water model. The accuracy of AB3 MFCT is quantified by the shape-preserving advection experiments in non-divergent flow, as well as a cosine bell whose shape changes during advection in shear flow. AB3 MFCT has been shown to be insensitive to time step size. This make AB3 MFCT an attractive transport scheme for explicit high resolution model applications with small time step. MFCT is tested in shallow-water model simulations to demonstrate that the use of MFCT maintains positive-definite tracer transport, while at the same time conserving both fluid mass and tracer mass within round-off errors in the AB3 dynamic core.