ANALYSIS ON A NUMERICAL SCHEME WITH SECOND-ORDER TIME ACCURACY FOR NONLINEAR DIFFUSION EQUATIONS

A nonlinear fully implicit finite difference scheme with second-order time evolution for nonlinear diffusion problem is studied.The scheme is constructed with two-layer coupled discretization(TLCD)at each time step.It does not stir numerical oscillation,while permits large time step length,and produces more accurate numerical solutions than the other two well-known second-order time evolution nonlinear schemes,the Crank-Nicolson(CN)scheme and the backward difference formula second-order(BDF2)scheme.By developing a new reasoning technique,we overcome the difficulties caused by the coupled nonlinear discrete diffusion operators at different time layers,and prove rigorously the TLCD scheme is uniquely solvable,unconditionally stable,and has second-order convergence in both s-pace and time.Numerical tests verify the theoretical results,and illustrate its superiority over the CN and BDF2 schemes.

A Novel Staggered Semi-implicit Space-Time Discontinuous Galerkin Method for the Incompressible Navier-Stokes Equations

A new high-order accurate staggered semi-implicit space-time discontinuous Galerkin(DG)method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space dimensions.The staggered DG scheme defines the discrete pressure on the primal triangular mesh,while the discrete velocity is defined on a staggered edge-based dual quadrilateral mesh.In this paper,a new pair of equal-order-interpolation velocity-pressure finite elements is proposed.On the primary triangular mesh(the pressure elements),the basis functions are piecewise polynomials of degree N and are allowed to jump on the boundaries of each triangle.On the dual mesh instead(the velocity elements),the basis functions consist in the union of piecewise polynomials of degree N on the two subtriangles that compose each quadrilateral and are allowed to jump only on the dual element boundaries,while they are continuous inside.In other words,the basis functions on the dual mesh arc built by continuous finite elements on the subtriangles.This choice allows the construction of an efficient,quadrature-free and memory saving algorithm.In our coupled space-time pressure correction formulation for the incompressible Navier-Stokes equations,the arbitrary high order of accuracy in time is achieved through tire use of time-dependent test and basis functions,in combination with simple and efficient Picard iterations.Several numerical tests on classical benchmarks confirm that the proposed method outperforms existing staggered semi-implicit space-time DG schemes,not only from a computer memory point of view,but also concerning the computational time.

Circular Scale of Time as a Guide for the Schrodinger Perturbation Process of a Quantum-Mechanical System

We point out that a suitable scale of time for the Schrödinger perturbation process is a closed line having rather a circular and not a conventional straight-linear character. A circular nature of the scale concerns especially the time associated with a particular order N of the perturbation energy which provides us with a full number of the perturbation terms predicted by Huby and Tong. On the other hand, a change of the order N—connected with an increased number of the special time points considered on the scale—requires a progressive character of time. A classification of the perturbation terms is done with the aid of the time-point contractions present on a scale characteristic for each N. This selection of terms can be simplified by a partition procedure of the integer numbers representing N-1. The detailed calculations are performed for the perturbation energy of orders N=7 and N=8 .

Effect of time bin size on accuracy of streak tube imaging lidar

Streak tube imaging lidar （STIL） is an active imaging system that has a high range accuracy with tile use of a pulsed lapser transmitter and streak tube receiver to produce 3D range inlages. This work investigates the effect of tile time bin size oil the range accuracy of STIL systems based on the peak detection algorithm. The nunlerical simulation indicates that the time bin size has a significant effect on the range aceuracy, resulting in a modified analytical estimate of the range error. An indoor experilnent with a planar target is carried out to validate the theory that shows the linear relationship between tile range error and the time bin size. Finer 3D depth iinages of a fist model are acquired by using a smaller time bin size and the best range error of 0.003 In is achieved with the optimal time bin size of 0.07 ns.

Implementation of a Multi-sampling-frequency System for RR-interval Timing and Blood Pressure Detection

In order to analyze the experimental cardiovascular signal with high accuracy, a system, integrating real-time monitoring and off-line further analysis, was developed and verified. The design, data processing and analysis methods as well as testing results are described. With 5 sampling frequency choices and 8 channel data acquisition, the system achieved high performances in beat-to-beat monitoring, signal processing and analysis. Tests were carried out to validate its performance in real-time monitoring, effectiveness of digital filters, QRS and blood pressure detection reliability, and RR-interval timing accuracy. The QRS detection rate was at least 99.46% for the records with few noises from MIT-BIH arrhythmia database using the algorithm for real-time monitoring, and no less than 96.43% for the records with some noises. In the condition that noise amplitude levels were less than 80%,the standard deviations for RR-interval timing were less than 1 ms with a generated ECG corrupted with various noises from MIT-BIH Noise Stress Test Database. Besides, the system is open for function expansion to meet further study-specific needs.

Accuracy for superposition of squeezed states in lossless and dissipative channel

The analysis of accuracy for superposition of squeezed states （SSSs） in lossless and loss case has been performed in this study. In lossless case, time accuracies of SSSs with mean photon number ns have a scaling of ns-2 in two limits of large and small squeezing. With the help of photon loss model, the dissipative channel will degrade accuracies has been proved. In the limit of large squeezing, the accuracy will slowly decrease with the reduction of transmittance η. In the limit of small squeezing, time accuracy scales as 1/（η4n2） and will decrease much faster along with η decreases.

Applications of two-way satellite time and frequency transfer in the BeiDou navigation satellite system

A two-way satellite time and frequency transfer(TWSTFT) device equipped in the BeiDou navigation satellite system(BDS)can calculate clock error between satellite and ground master clock. TWSTFT is a real-time method with high accuracy because most system errors such as orbital error, station position error, and tropospheric and ionospheric delay error can be eliminated by calculating the two-way pseudorange difference. Another method, the multi-satellite precision orbit determination(MPOD)method, can be applied to estimate satellite clock errors. By comparison with MPOD clock estimations, this paper discusses the applications of the BDS TWSTFT clock observations in satellite clock measurement, satellite clock prediction, navigation system time monitor, and satellite clock performance assessment in orbit. The results show that with TWSTFT clock observations, the accuracy of satellite clock prediction is higher than MPOD. Five continuous weeks of comparisons with three international GNSS Service(IGS) analysis centers(ACs) show that the reference time difference between BeiDou time(BDT) and golbal positoning system(GPS) time(GPST) realized IGS ACs is in the tens of nanoseconds. Applying the TWSTFT clock error observations may obtain more accurate satellite clock performance evaluation in the 104 s interval because the accuracy of the MPOD clock estimation is not sufficiently high. By comparing the BDS and GPS satellite clock performance, we found that the BDS clock stability at the 103 s interval is approximately 10.12, which is similar to the GPS IIR.

High Order Accurate Direct Arbitrary-Lagrangian-Eulerian ADER-MOOD Finite Volume Schemes for Non-Conservative Hyperbolic Systems with Stiff Source Terms

In this paper we present a 2D/3D high order accurate finite volume scheme in the context of direct Arbitrary-Lagrangian-Eulerian algorithms for general hyperbolic systems of partial differential equations with non-conservative products and stiff source terms.This scheme is constructed with a single stencil polynomial reconstruction operator,a one-step space-time ADER integration which is suitably designed for dealing even with stiff sources,a nodal solver with relaxation to determine the mesh motion,a path-conservative integration technique for the treatment of non-conservative products and an a posteriori stabilization procedure derived from the so-called Multidimensional Optimal Order Detection(MOOD)paradigm.In this work we consider the seven equation Baer-Nunziato model of compressible multi-phase flows as a representative model involving non-conservative products as well as relaxation source terms which are allowed to become stiff.The new scheme is validated against a set of test cases on 2D/3D unstructured moving meshes on parallel machines and the high order of accuracy achieved by the method is demonstrated by performing a numerical convergence study.Classical Riemann problems and explosion problems with exact solutions are simulated in 2D and 3D.The overall numerical code is also profiled to provide an estimate of the computational cost required by each component of the whole algorithm.

New 0D/1D Physical Approach for Modelling the Gas Dynamics Behavior Inside the Intake System of an Engine

The competition among carmakers to introduce the most innovative solutions is growing day by day. Since few years, simulation is being used widely in automotive industries. Instead of building costly prototypes and expending fuel for doing tests on a real engine, simulation became a good solution before taking new decisions. Concerning the study of gas dynamics and pressure wave's propagation in the intake system of an internal combustion engine, a precise modelling is needed in order to obtain good results. Unfortunately, the computational time for these simulations is considered as high compared to the real time. The main objective of the new approach presented in this paper, is to reduce simulation time of models in the internal combustion engine simulation code, allowing them to accomplish many engine simulations faster than one-dimensional non-linear approach. A transfer function is defined to link directly the relative pressure and the air mass flow rate. In a second time, the model is included into an internal combustion engine simulation code. The results obtained with this code are compared to experimental ones which are measured on a one-cylinder engine test bench. A good agreement is obtained between the experimental results and the numerical one. The model was improved by adding a transfer function for temperature evolution. The convergence time is then reduced as well as the global simulation time of the model.