RKDG Methods with Multi-resolution WENO Limiters for Solving Steady-State Problems on Triangular Meshes

In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constructed to identify triangular cells in which the application of the limiting procedures is required. In such troubled cells, the multi-resolution WENO limiting methods are used to the hierarchical L^(2) projection polynomial sequence of the DG solution. Through using the RKDG methods with multi-resolution WENO limiters, the optimal high-order accuracy can be gradually reduced to first-order in the triangular troubled cells, so that the shock wave oscillations can be well suppressed. In steady-state simulations on triangular meshes, the numerical residual converges to near machine zero. The proposed spatial reconstruction methods enhance the robustness of classical DG methods on triangular meshes. The good results of these RKDG methods with multi-resolution WENO limiters are verified by a series of two-dimensional steady-state problems.

Revisting High-Resolution Schemes with van Albada Slope Limiter

Slope limiters play an essential role in maintaining the non-oscillatory behavior of high-resolution methods for nonlinear conservation laws.The family of minmod limiters serves as the prototype example.Here,we revisit the question of non-oscillatory behavior of high-resolution central schemes in terms of the slope limiter proposed by van Albada et al.(Astron Astrophys 108:76–84,1982).The van Albada(vA)limiter is smoother near extrema,and consequently,in many cases,it outperforms the results obtained using the standard minmod limiter.In particular,we prove that the vA limiter ensures the one-dimensional Total-Variation Diminishing(TVD)stability and demonstrate that it yields noticeable improvement in computation of one-and two-dimensional systems.

Neural Network-Based Limiter with Transfer Learning

Recent works have shown that neural networks are promising parameter-free limiters for a variety of numerical schemes(Morgan et al.in A machine learning approach for detect-ing shocks with high-order hydrodynamic methods.et al.in J Comput Phys 367:166-191.,2018;Veiga et al.in European Conference on Computational Mechanics andⅦEuropean Conference on Computational Fluid Dynamics,vol.1,pp.2525-2550.ECCM.,2018).Following this trend,we train a neural network to serve as a shock-indicator function using simulation data from a Runge-Kutta discontinuous Galer-kin(RKDG)method and a modal high-order limiter(Krivodonova in J Comput Phys 226:879-896.,2007).With this methodology,we obtain one-and two-dimensional black-box shock-indicators which are then coupled to a standard limiter.Furthermore,we describe a strategy to transfer the shock-indicator to a residual distribution(RD)scheme without the need for a full training cycle and large data-set,by finding a mapping between the solution feature spaces from an RD scheme to an RKDG scheme,both in one-and two-dimensional problems,and on Cartesian and unstruc-tured meshes.We report on the quality of the numerical solutions when using the neural network shock-indicator coupled to a limiter,comparing its performance to traditional lim-iters,for both RKDG and RD schemes.

Study on the formation of arc plasma on the resistive wall liquid metal current limiter

Due to its significant attributes,the liquid metal current limiter(LMCL)is considered a new strategy for limiting short-circuit current in the power grid.A resistive wall liquid metal current limiter(RWLMCL)is designed to advance the starting current-limiting time.Experiments are performed to investigate the dynamic behaviors of liquid metal,and the influence of different currents on the liquid metal self-shrinkage effect is compared and analyzed.Furthermore,the liquid metal self-shrinkage effect is mathematically modeled,and the reason for the formation of arc plasma is obtained by simulation.The laws of arc plasma formation and the current transfer in the cavity are revealed,and the motion mechanisms are explained by physical principles.The simulations are in accordance with the test data.It is demonstrated that the sudden change of the current density at both ends of the wall causes the liquid metal to shrink and depress under the electromagnetic force,and the current starts to transfer from the liquid metal path to the wall resistance path.The RWLMCL can effectively advance the starting current-limiting time.

On High-Resolution Entropy-Consistent Flux with Slope Limiter for Hyperbolic Conservation Laws

This paper proposes a new version of the high-resolution entropy-consistent(EC-Limited)flux for hyperbolic conservation laws based on a new minmod-type slope limiter.Firstly,we identify the numerical entropy production,a third-order differential term deduced from the previous work of Ismail and Roe[11].The corresponding dissipation term is added to the original Roe flux to achieve entropy consistency.The new,resultant entropy-consistent(EC)flux has a general and explicit analytical form without any corrective factor,making it easy to compute and a less-expensive method.The inequality constraints are imposed on the standard piece-wise quadratic reconstruction to enforce the pointwise values of bounded-type numerical solutions.We design the new minmod slope limiter as combining two separate limiters for left and right states.We propose the EC-Limited flux by adding this reconstruction data method to the primitive variables rather than to the conservative variables of the EC flux to preserve the equilibrium of the primitive variables.These resulting fluxes are easily applied to general hyperbolic conservation laws while having attractive features:entropy-stable,robust,and non-oscillatory.To illustrate the potential of these proposed fluxes,we show the applications to the Burgers equation and the Euler equations.

LEARNING ALGORITHM OF FEEDFORWARD NEURAL NETWORK WITH HARD LIMITER USED FOR CLASSIFICATION

A learning algorithm based on a hard limiter for feedforward neural networks (NN) is presented,and is applied in solving classification problems on separable convex sets and disjoint sets.It has been proved that the algorithm has stronger classification ability than that of the back propagation (BP) algorithm for the feedforward NN using sigmoid function by simulation.What is more,the models can be implemented with lower cost hardware than that of the BP NN.LEARNIN

A novel fault current limiter topology design based on liquid metal current limiter

The liquid metal current limiter(LMCL)is regarded as a viable solution for reducing the fault current in a power grid.But demonstrating the liquid metal arc plasma self-pinching process of the resistive wall,and reducing the erosion of the LMCL are challenging,not only theoretically,but also practically.In this work,a novel LMCL is designed with a resistive wall that can be connected to the current-limiting circuit inside the cavity.Specifically,a novel fault current limiter(FCL)topology is put forward where the novel LMCL is combined with a fast switch and current-limiting reactor.Further,the liquid metal self-pinch effect is modeled mathematically in three dimensions,and the gas-liquid two-phase dynamic diagrams under different short-circuit currents are obtained by simulation.The simulation results indicate that with the increase of current,the time for the liquid metal-free surface to begin depressing is reduced,and the position of the depression also changes.Different kinds of bubbles formed by the depressions gradually extend,squeeze,and break.With the increase of current,the liquid metal takes less time to break,but breaks still occur at the edge of the channel,forming arc plasma.Finally,relevant experiments are conducted for the novel FCL topology.The arcing process and current transfer process are analyzed in particular.Comparisons of the peak arc voltage,arcing time,current limiting efficiency,and electrode erosion are presented.The results demonstrate that the arc voltage of the novel FCL topology is reduced by more than 4.5times and the arcing time is reduced by more than 12%.The erosions of the liquid metal and electrodes are reduced.Moreover,the current limiting efficiency of the novel FCL topology is improved by 1%–5%.This work lays a foundation for the topology and optimal design of the LMCL.

Investigation on the Arc Ignition Characteristics and Energy Absorption of Liquid Metal Current Limiter Based on Self-Pinch Effect

The GaInSn liquid metal current limiter based on the fluid pinch effect has broad application prospects due to its particular properties. However, the limited rated current and abil- ity of power dissipation are the critical problems for its wide application. Firstly, the temperature distribution of the liquid metal current limiter （LMCL） was obtained by experiments with a rated current of 1 kA and the arc ignition phenomenon was observed with 1.5 kA, which indicates that the rated current is mainly limited by the arc rather than the high temperature compared to the traditional switchgears. Furthermore, an improved method is proposed by adding the paralleled pure resistance, impedance or another LMCL element to protect the setup from the fault energy concentration in the setup. The problem of a slower arc voltage increasing rate can be solved by adding a paralleled impedance with suitable parameters. Finally, the current limiting properties based on the improved method were investigated and the alternating oscillating current was found between two paralleled LMCL elements owing to their deviation of arc ignition in reality.

Hermite WENO-based limiters for high order discontinuous Galerkin method on unstructured grids

A novel class of weighted essentially nonoscillatory （WENO） schemes based on Hermite polynomi- als, termed as HWENO schemes, is developed and applied as limiters for high order discontinuous Galerkin （DG） method on triangular grids. The developed HWENO methodology utilizes high-order derivative information to keep WENO re- construction stencils in the von Neumann neighborhood. A simple and efficient technique is also proposed to enhance the smoothness of the existing stencils, making higher-order scheme stable and simplifying the reconstruction process at the same time. The resulting HWENO-based limiters are as compact as the underlying DG schemes and therefore easy to implement. Numerical results for a wide range of flow conditions demonstrate that for DG schemes of up to fourth order of accuracy, the designed HWENO limiters can simul- taneously obtain uniform high order accuracy and sharp, es- sentially non-oscillatory shock transition.

Study of total variation diminishing (TVD) slope limiters in dam-break flow simulation

A two-dimensional （2D） dam-break flow numerical model was developed based on the finite-volume total variation diminishing （TVD） and monotone upstream-centered scheme for conservation laws （MUSCL）-Hancock scheme, which has second-order accuracy in both time and space. A Harten-Lax-van Leer-contact （HLLC） approximate Riemann solver was used to evaluate fluxes. The TVD MUSCL-Hancock numerical scheme utilizes slope limiters, such as the minmod, double minmod, superbee, van Albada, and van Leer limiters, to prevent spurious oscillations and maintain monotonicity near discontinuities. A comparative study of the impact of various slope limiters on the accuracy of the numerical flow model was conducted with several dam-break examples including wet and dry bed cases. The numerical results of the superbee and double minmod limiters agree better with the theoretical solution and have higher accuracy than other limiters in one-dimensional （1D） space. The ratio of the downstream water depth to the upstream water depth was used to select the proper slope limiter. For the 2D numerical model, the superbee limiter should not be used, owing to significant numerical dispersion.

Plasma Limiter Based on Surface Wave Plasma Excited by Microwave

A novel plasma limiter, in which the plasma is excited by surface wave, is presented. The breakdown time of some gases filled in the limiter were calculated as a function of gas pres- sure, ionization degree and density of seed electrons under low pressure （0.01 -1 Torr） and high pressure （10 -1000 Torr） cases. The results show that the limiter filled with Xe with a pressure of 0.9 Torr, seed electron density of 10^16 m^-3, and ionization degree of 10^-4, has a breakdown time of approximate 19.6 ns.

Evidence of vapor shielding effect on heat flux loaded on flowing liquid lithium limiter in EAST

A lithium(Li)vapour layer was formed around a flowing liquid Li limiter to shield against the plasma incident power and reduce limiter heat flux in the EAST tokamak.The results revealed that after a plasma operation of a few seconds,the layer became clear,which indicated a strong Li emission with a decrease in the limiter surface temperature.This emission resulted in a dense vapour around the limiter,and Li ions moved along the magnetic fleld to form a green shielding layer on the limiter.The plasma heat flux loaded on the limiter,measured by the probe installed on the limiter,was approximately 52%lower than that detected by a fast-reciprocating probe at the same radial position without the limiter in EAST.Additionally,approximately 42%of the parallel heat flux was dissipated directly with the enhanced Li radiation in the discharge with the liquid metal infused trenches(LIMIT)limiter.This observation revealed that the Li vapour layer exhibited an excellent shielding effect to liquid Li on plasma heat flux,which is a possible beneflt of liquid-plasma-facing components in future fusion devices.

Study of the Fast-Closing Switch Used for Fault Current Limiters in Power System

This paper presents a new type of fault current limiter (FCL) based on fast closing switch, which is composed of a capacitor bank and a reactor in series. The main control component is a fast closing switch connected in parallel with the capacitors, which is driven by the electromagnetic repulsion force. It can response the order within 1 ms. When fault occurs, the switch closes and the capacitors are bypassed, and the fault current is limited by the reactor. Simulation analysis and experiment show that the electromagnetic repulsion force actuator can meet the demand of fast closing switch, it is feasible to develop the FCL with low cost and high reliability.

An Active Inrush Current Limiter Based on SCR Phase Shift Control for EV Charging Systems

This article gives an overview of the main passive solutions and active techniques, based on AC switches to limit inrush currents in medium power AC-DC converters （up to 3.7 kW） for electric vehicle charging systems. In particular, a strategy, based on SCR （silicon controlled rectifier） phase, shift control in a mixed rectifier bridge with diodes and thyristors, is proposed. The challenge is to help designers optimize the triggering delay of SCRs to both limit the peak value of inrush current spikes and optimize the charge duration of the DC-link capacitor. A mathematical model （Mathcad engineering tool） has been defined to point out, the interest of a variable triggering delay to control SCRs to meet the expectations described previously. Experimental measurements using an industrial evaluation board of the AC-DC converter demonstrate the robustness of the method.

Hybrid Operation of Fault Current Limiter and Thyristor Controlled Braking Resistor

The effectiveness of a combination of fault current limiter and thyristor controlled braking resistor on power system stability enhancement and damping turbine shaft torsional oscillations has been studied. If both devices operate at the same bus, the stabilization control scheme can be carried out continuously and with flexibility. As a result, the fault currents are limited, and the generator disturbances and the turbine shaft torsional oscillations are converged quickly. In this paper, the effectiveness of the combination of both devices has been demonstrated by considering 3LG （three-lines-to-ground） fault in a two-machine infinite bus system. Also, temperature rise effect of both devices with various resistance values and weights has been demonstrated. Simulation results indicate a significant power system stability enhancement and damping turbine shaft torsional oscillations as well as with allowable temperature rise.

The application of limiter target electrostatic measurement system in J-TEXT tokamak

The limiter target electrostatic measurement system including limiter grounding current sensors and Langmuir probes have been newly developed for the measurement of the limiter target area on the Joint-Texas Experimental tokamak (J-TEXT). Current sensors fixed between graphite limiters and the vacuum vessel walls are used to measure the currents between limiters and vessel wall. Simultaneously, a rectangular poloidal array containing 54 Langmuir probes is embedded in the graphite tiles of limiters for a more localized measurement. Based on this system, the effect of both the plasma’s inherent behavior, including plasma motion and the 2/1 tearing mode, and the electrode biasing on probe and sensor signals have been observed and analyzed in the experiments.

Flux Limiter Lattice Boltzmann for Compressible Flows

In this paper, a new flux limiter scheme with the splitting technique is successfully incorporated into a multiple-relaxation-time lattice Boltzmann （LB） model for shacked compressible flows. The proposed flux limiter scheme is efficient in decreasing the artificial oscillations and numerical diffusion around the interface. Due to the kinetic nature, some interface problems being difficult to handle at the macroscopic level can be modeled more naturally through the LB method. Numerical simulations for the Richtmyer-Meshkov instability show that with the new model the computed interfaces are smoother and more consistent with physical analysis. The growth rates of bubble and spike present a satisfying agreement with the theoretical predictions and other numerical simulations.

Flux Limiter Lattice Boltzmann Scheme Approach to Compressible Flows with Flexible Specific-Heat Ratio and Prandtl Number

We further develop the lattice Boltzmann （LB） model [Physica A 382 （2007） 502] for compressible flows from two aspects. Firstly, we modify the Bhatnagar Gross Krook （BGK） collision term in the LB equation, which makes the model suitable for simulating flows with different Prandtl numbers. Secondly, the flux limiter finite difference （FLFD） scheme is employed to calculate the convection term of the LB equation, which makes the unphysical oscillations at discontinuities be effectively suppressed and the numerical dissipations be significantly diminished. The proposed model is validated by recovering results of some well-known benchmarks, including （i） The thermal Couette flow; （ii） One- and two-dlmenslonal FLiemann problems. Good agreements are obtained between LB results and the exact ones or previously reported solutions. The flexibility, together with the high accuracy of the new model, endows the proposed model considerable potential for tracking some long-standing problems and for investigating nonlinear nonequilibrium complex systems.

Numerical Investigation of Heat Deposition Patterns on the Surface of HT-7 Actively Cooled Toroidal Limiter

Two water cooled toroidal limiters were used in HT-7 to exhaust power effectively since the spring campaign of 2004. The heat flux deposition pattern on their surfaces both in steady state and transient state, caused only by plasma displacement, were studied with ANSYS code. The ripple of the toroidal magnetic field was taken into account. The heat flux deposition appeared to be periodic. The ripple and the relative location of the limiter to the toroidal field （TF） coils, as well as the shift of the center of the last closed flux surface （LCFS）, had a vital influence upon the heat flux profile. The location with maximum temperature didn＇t coincide with that for the maximum heat flux in a transient state. The shift of the center of LCFS, caused by plasma displacement, made the heat flux on the limiter more uneven. The heat flux deposition pattern concerning the real shift of the center of LCFS at a transient state calls for further research.

Placement optimization of Multi-Type fault current limiters based on genetic algorithm

The fault current limiter(FCL)is an effective measure for improving system stability and suppressing short-circuit fault current.Because of space and economic costs,the optimum placement of FCLs is vital in industrial applications.In this study,two objectives with the same dimensional measurement unit,namely,the total capital investment cost of FCLs and circuit breaker loss related to short-circuit currents,are considered.The circuit breaker loss model is developed based on the attenuation rule of the circuit breaker service life.The circuit breaker loss is used to quantify the current-limiting effect to avoid the problem of weight selection in a multi-objective problem.The IEEE 10-generator 39-bus system in New England is used to evaluate the performance of the proposed genetic algorithm(GA)method.Comparative and sensitivity analyses are performed.The results of the optimized plan are validated through simulations,indicating the significant potential of the GA for such optimization.