Efficient Transient Simulation Research Articles

A Novel Approach Integrating the Method of Characteristics with Large Time-Step Scheme (MOC-LTS) for Efficient Transient Flow Simulation in Liquid Pipelines

Water hammer incidents pose a significant risk to the safety and stability of pipeline operations. Therefore, rapid and precise transient flow simulation is essential for efficiently developing scientific water hammer control strategies. Nevertheless, the prevailing transient flow simulation methods for liquid pipelines predominantly employ explicit schemes to solve transient flow control equations, necessitating adherence to the stability criterion of Courant-Friedrichs-Lewy (CFL) ≤ 1. This results in limited time step sizes, which in turn constrains computational efficiency, particularly when simulating hydraulic behavior in large-scale pipeline networks. In this paper, a novel approach integrating the method of characteristics (MOC) with a large time-step scheme (LTS) is proposed to enable rapid and accurate simulation of transient flow in liquid pipelines. The proposed approach discretizes the computational domain into contiguous control volumes, ategorizing them as either boundary or internal control volumes depending on whether they are affected by boundary conditions within a large time step. For internal control volumes, an LTS scheme based on the first-order Godunov format is employed to improve computational efficiency. For boundary control volumes, MOC is applied iteratively to accurately capture boundary dynamics until the simulated time matches that of the internal control volumes. Quantitative analysis is conducted to verify the performance of the proposed approach. The results confirm that the proposed approach outperforms the MOC in computational efficiency while maintaining minimal accuracy loss.

Model order reduction of time-domain acoustic finite element simulations with perfectly matched layers

This paper presents a stability-preserving model reduction method for an acoustic finite element model with perfectly matched layers (PMLs). PMLs are often introduced into an unbounded domain to simulate the Sommerfeld radiation condition. These layers act as anisotropic damping materials to absorb the scattered field, of which the material properties are frequency- and coordinate-dependent. The corresponding time-domain model size is often very large due to this frequency-dependent property and the number of elements needed per wavelength. Therefore, to enable efficient transient simulations, this paper proposes a two-step method to generate stable reduced order models (ROMs) of such systems. Firstly, the modified and stable version of PMLs is projected by a one-sided split basis, which gives a stable intermediate ROM. Secondly, the intermediate ROM is modified to satisfy the stability-preserving condition by applying the modal transformation. Applying any one-sided model order reduction method on this modified model leads to a stable and small ROM. This two-step method is further extended to account for the locally-conformal PML model by reformulating it in curvilinear coordinates, which works for arbitrary convex truncated domains. The proposed method is successfully verified by several numerical simulations.

Dynamic phasor-based hybrid simulation for multi-inverter grid-connected system

To realize the efficient transient simulation of a grid-connected power generation system based on multiple inverters, this paper proposes a hybrid simulation method integrating the models of electromagnetic transient and dynamic phasors. Based on a demonstration of the concepts and properties of dynamic phasors, the models of single-phase and three-phase inverters described by dynamic phasors are established first. Considering the numerical compatibility problem between dynamic phasors and instantaneous values, an interface scheme between dynamic phasors and instantaneous values is designed, and the efficiency and precision differences of various transformation methods are compared in detail. Finally, by utilizing MATLAB/Simulink, a hybrid simulation platform of a multi-inverter grid-connected system is built, and the efficiency and accuracy of the hybrid simulation are validated via comparison with the full electromagnetic transient simulation.

Black box stability preserving reduction techniques in the Loewner framework for the efficient time domain simulation of dynamical systems with damping treatments

New applications, such as material characterization, auralization and virtual sensing, have renewed the need and interest in efficient transient time-domain simulations of dynamical systems. However, the typical required numerical simulations for these applications are cumbersome to compute due to the high computational burden involved in the calculation of mechanical systems. Model order reduction techniques are important enablers to reduce this computation time. However, many reduction techniques fail when viscous or thermal damping is present in the system. This work elaborates on two non-intrusive reduction techniques using the Loewner framework which can serve as a tool for the efficient time domain simulation of second order dynamical systems with damping treatments. The reduced models are constructed using frequency domain data, however, for time domain simulations, the reduced models need to be real-valued and stable. One methodology exploits the well-known inverse fast Fourier transform, while the second methodology employs a reduced order model which serves as an input for a time marching technique. Although the Loewner reduction technique does not preserve the stability of the original system, both proposed methodologies show to be able to return an accurate and sufficiently stable time domain response.

A workflow leveraging MOOSE transient multiphysics simulations to evaluate the impact of thermophysical property uncertainties on molten-salt reactors

A new approach is proposed to evaluate the safety of molten-salt reactors (MSRs), using advanced modeling and simulation (M&S) tools. This approach augments the Monitoring and Inspection (M&I) concept for fuel qualification by enabling computation of the change in critical safety parameters as a result of altered thermo-physical fuel properties. This work uses newly developed capabilities in the MOOSE framework to perform the requisite M&S. The neutronics code Griffin, using its neutron diffusion solver, is coupled to the coarse-mesh, multi-dimensional, thermal-hydraulic capabilities of Pronghorn. The resulting new capability enables efficient transient multiphysics simulations of open-pool-type MSR concepts, including delayed neutron precursor advection and beyond design basis events. The proposed approach uses the coupled Griffin/Pronghorn models to perform a sensitivity analysis by perturbing the salt thermophysical properties and evaluating the resulting impact on key safety parameters during an unprotected loss-of-forced-flow accident. In light of the challenges associated with predicting the effect of reactor operations and burnup on bulk salt properties, this work demonstrates how Griffin/Pronghorn multiphysics simulations may be used to evaluate whether changes in salt properties could potentially lead to unsafe reactor configurations.

Efficient transient thermal simulation with Laguerre-based finite-element method and domain decomposition

In this article, a Laguerre-based finite-element method (LBFEM) combined with domain decomposition is proposed for large-scale transient thermal simulation. The unconditionally stable marching-on-in-order scheme is obtained using the weighted Laguerre polynomials and Galerkin testing procedure to eliminate the time variable of the temperature field. An effective data filtering method is utilized to reduce the number of basis functions and improve the efficiency of simulation. To handle the large-scale problems, a domain decomposition scheme named finite element tearing and interconnecting (FETI) is applied. The entire computational domain can be divided into a series of small-scale subdomains to reduce the computational resources. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method.

Deflated Restarting of Exponential Integrator Method with an Implicit Regularization for Efficient Transient Circuit Simulation

Exponential integrator (EI) method based on Krylov subspace approximation is a promising method for large-scale transient circuit simulation. However, it suffers from the singularity problem and consumes large subspace dimensions for stiff circuits when using the ordinary Krylov subspace. Restarting schemes are commonly applied to reduce the subspace dimension, but they also slow down the convergence and degrade the overall computational efficiency. In this paper, we first devise an implicit and sparsity-preserving regularization technique to tackle the singularity problem facing EI in the ordinary Krylov subspace framework. Next, we analyze the root cause of the slow convergence of the ordinary Krylov subspace methods when applied to stiff circuits. Based on the analysis, we propose a deflated restarting scheme, compatible with the above regularization technique, to accelerate the convergence of restarted Krylov subspace approximation for EI methods. Numerical experiments demonstrate the effectiveness of the proposed regularization technique, and up to 50% convergence improvements for Krylov subspace approximation compared to the non-deflated version.

Wave Function and Multiscale Modeling of MMC-HVdc System for Wide-Frequency Transient Simulation

The detailed modeling of power electronic (PE) devices poses challenging problems to an efficient transient simulation of large-scale PE-dominated power systems. As PE paradigm, a multiscale modeling methodology of the modular multilevel converter (MMC) for simulating diverse transients from low-frequency oscillations up to high-frequency switching events in an MMC high-voltage direct current (HVdc) system is developed, implemented, and validated. The novelty lies in the creation of a wave propagation function (WPF) that describes the MMC submodule (SM) transient behavior, and then, the SM Fourier series-based shifted-frequency phasor (SFP) is developed to accelerate the computation speed of the system-level dynamics. These efforts serve as the basis for multiscale modeling of the MMC where a multiple-frequency shifting is achieved. By implementing a seamless model interface with the control systems, the multiscale modeling is applicable to an MMC-HVdc transmission system. The multiscale model is validated through case studies that cover dc fault, MMC internal fault, power oscillations, and wind power fluctuations. The computational accuracy and efficiency of the model are verified through a comparison of the results with those from the full electromagnetic transient (EMT) model.

Comprehensive Modeling of Large Photovoltaic Systems for Heterogeneous Parallel Transient Simulation of Integrated AC/DC Grid

Detailed nonlinear transient modeling of the photovoltaic (PV) system enables an accurate study of the host integrated AC/DC grid. In this article, the parallel architecture of the graphics processing unit (GPU) catering to a massive number of PV modules is utilized in conjunction with CPU for efficient transient simulation. To reflect the exact operation status of the solar power system subjected to various temperatures and nonuniform solar irradiance in the electromagnetic transient (EMT) simulation, all necessary panels are modeled individually, and therefore, a scalable PV array model with a flexible level of aggregation is proposed in addition to its fully detailed discrete counterpart so as to improve the computational efficiency. The single-instruction multiple-thread implementation mode of the GPU enables up to 10 million PV panels, regardless of the size or type, to be computed concurrently, and noticing that the hybrid AC/DC grid has a significant irregularity, the CPU is also adopted to tackle systems with inadequate parallelism. Meanwhile, since the AC grid dynamic interaction has a distinct tolerance on the time-step to that of the remaining part, a multi-rate scheme is employed to expedite the heterogeneous CPU-GPU computation for dynamic-EMT co-simulation, whose results are validated by the commercial off-line tools MATLAB/Simulink and DSATools/TSAT.

Simulation of Thermoelastic Problems with the Finite Element Method

AbstractDisc brakes convert kinetic energy into thermal energy in order to slow down vehicles. During the braking process enormous heat flows and temperature gradients occur in the system. Because heating leads to a change in shape for most materials, it is important to take the temperature and its influence into account during the design process. The interaction between the structure and the heat in disc brakes can be described with methods from thermoelasticity. To simulate thermoelastic behaviour the Finite Element Method is commonly used. The thermal and mechanical domain are taken into account by coupling the equation of motion and the heat equation. However, in transient analysis often the problem occurs of different time scales of the structural and thermal dynamics for many technically relevant materials, like steel. For metallic materials the time constant of structural dynamics is much smaller than those of thermal dynamics. This complicates an efficient transient simulation. In the present work the implementation of a Finite Element Method in thermoelasticity and associated investigations are shown. The method is applied to various parts and load cases. Also different approaches to deal with the different time scales will be shown. Heuristic methods like mass‐scaling as well as more mathematically oriented approaches like model order reduction are presented.

Pole-Zero Identification: Unveiling the Critical Dynamics of Microwave Circuits Beyond Stability Analysis

The term pole-zero identification refers to obtaining the poles and zeros of a linear (or linearized) system described by its frequency response. This is usually done using optimization techniques (such as least squares, maximum likelihood estimation, or vector fitting) that fit a given frequency response of the linear system to a transfer function defined as the ratio of two polynomials [1], [2]. This kind of linear system identification in the frequency domain has numerous applications in a wide variety of engineering fields, such as mechanical systems, power systems, and electromagnetic compatibility. In the microwave domain, rational approximation is increasingly used to obtain black-box models of complex passive structures for model order reduction and efficient transient simulation. An extensive bibliography on the matter can be found in [3]-[6]. In this article, we focus on a different application of pole-zero identification. We review the different ways in which pole-zero identification can be applied to nonlinear circuit design, for power-amplifier stability analysis, and more. We provide a comprehensive view of recent approaches through illustrative application examples. Other uses for rational-approximation techniques are beyond the scope of this article.

An efficient transient simulation procedure for the reliable estimation of draft tube losses in the hydraulic design process

Draft tube flow plays a significant role for the overall performance of a hydraulic machine and requires therefore special attention in the design process. However, as it is characterized by complex flow phenomena like swirl, adverse pressure gradients and flow separation, accurate predictions are challenging. Though the required technologies like transient simulation techniques and adequate turbulence modeling are available, it is especially the tremendous time consumption that renders the according analysis infeasible for the hydraulic design process.In this contribution a new simulation methodology is presented that accelerates transient simulations in three ways. Firstly, the computational domain is significantly reduced by substituting the distributor with appropriate boundary conditions. Secondly, it is shown by a grid study that meshes with intermediate resolutions are to be favored over massively refined grids. And thirdly, a timestep study uncovers potential for increased step sizes. The proposed methodology is validated by comparison to PIV measurements performed by Frey et al. (IOP Conf. Ser.: Earth and Env. Sci. 49 082007), thus demonstrating that the developed workflow yields accurate and reliable results.

Efficiency enhancement method without grid partitioning for hard real‐time transient simulation of large power grids

Efficient transient simulation of large power grid is of great importance for system operation and dispatching, fault repetition, operator training etc. Online stability estimation and testing on system control and protection require hard real-time performance of transient simulation. The conventional real-time simulation, which splits an entire grid into sub-grids and solves them in parallel, lacks generality for various case systems. This study proposes a new efficiency enhancement method without grid partitioning. Three key techniques are involved. First, parallel solving format is proposed to distribute two-layer computational burdens into central processing unit cores in balance. Second, to calculate the fault changing the grid structure, the inverse current compensation is employed instead of re-forming impedance matrix and repeating lower-upper (LU) decomposition. Third, dual-loop forward and backward substitutions to solve grid equations are modified to a single-loop iteration, which further improves the computational efficiency. At last, the validity and effectiveness of the proposed method are verified by tests.

A theoretical study on tunneling based biosensor having a redox-active monolayer using physics based simulation

We developed a numerical simulator to model the operation of a tunneling based biosensor which has a redox-active monolayer. The simulator takes a realistic device structure as a simulation domain, and it employs the drift-diffusion equation for ion transport, the non-equilibrium Green's function formalism for electron tunneling, and the Ramo-Shockley theorem for accurate calculation of non-faradaic current. We also accounted for the buffer reaction and the immobilized peptide layer. For efficient transient simulation, the implicit time integration scheme is employed where the solution at each time step is obtained from the coupled Newton-Raphson method. As an application, we studied the operation of a recently fabricated reference-electrode free biosensor in various bias conditions and confirmed the effect of buffer reaction and the current flowing mechanism. Using the simulator, we also found a strategy to maximize the sensitivity of the tunneling based sensor.

A Projective Integration Method for Transient Stability Assessment of Power Systems With a High Penetration of Distributed Generation

The impact of numerous distributed generators (DGs) coupled with the implementation of virtual inertia on the transient stability of power systems has been studied extensively. Time-domain simulation is the most accurate and reliable approach to evaluate the dynamic behavior of power systems. However, the computational efficiency is restricted by their multi-time-scale property due to the combination of various DGs and synchronous generators. This paper presents a novel projective integration method (PIM) for the efficient transient stability simulation of power systems with high DG penetration. One procedure of the proposed PIM is decomposed into two stages, which adopt mixed explicit-implicit integration methods to achieve both efficiency and numerical stability. Moreover, the stability of the PIM is not affected by its parameter, which is related to the step size. Based on this property, an adaptive parameter scheme is developed based on error estimation to fit the time constants of the system dynamics and further increase the simulation speed. The presented approach is several times faster than the conventional integration methods with a similar level of accuracy. The proposed method is demonstrated using test systems with DGs and virtual synchronous generators, and the performance is verified against MATLAB/Simulink and DIgSILENT PowerFactory.

Fast alternating direction implicit method for efficient transient thermal simulation of integrated circuits

SummaryThis paper presents fast alternating direction implicit (FADI) method for efficient transient thermal simulation of integrated circuits. The FADI method is formulated from Peaceman–Rachford's ADI and Douglas–Gunn's ADI methods. The update procedure of the proposed method has basic implicit form that features derivative‐free right‐hand side and hence, better efficiency and conciseness. Subsequently, through the basic implicit form of FADI method, the relationship between classical Peaceman–Rachford's and Douglas–Gunn's ADI methods can be clarified and elucidated in detail. A unified boundary condition that can cater to common kinds of boundary conditions in thermal simulation is also introduced. To further accelerate FADI method, the graphics processing unit is also utilized through Compute Unified Device Architecture implementation. It is shown that high efficiency gain can be achieved using the proposed FADI method through large time step size and data parallelism, while maintaining stability and good accuracy. As numerical illustration, an integrated circuit structure with microchannel cooling is demonstrated. Numerical results further ascertain the cooling effect of the microchannels. Copyright © 2015 John Wiley & Sons, Ltd.

Efficient Simulation of Gear Contacts Including Transient Elastohydrodynamic Effects

This paper describes an efficient transient elastohydrodynamic simulation method for gear contacts. The model uses oil films and elastic deformations directly in the multibody simulation, and is based on the Reynolds equation including squeeze and wedge terms as well as an elastic half-space. Two transient solutions to this problem, an analytical and a numerical one, were developed. The analytical solution is accomplished using assumptions for the gap shape and the pressure in the middle of the gap. The numerical problem is solved using multilevel multi-integration algorithms. With this approach, tooth impacts during gear rattling as well as highly loaded power-transmitting gear contacts can be investigated and lubrication conditions like gap heights or type of friction may be determined. The method was implemented in the multibody simulation environment SIMPACK. Therefore it is easy to transfer the developed element to other models and use it for a multitude of different engineering problems. A detailed three-dimensional elastic multibody model of an experimental transmission is used to validate the developed method. Important values of the gear contact like normal and tangential forces, proportion of dry friction, and minimum gap heights are calculated and studied for different conditions. In addition, pressure distributions on tooth flanks as well as gap forms are determined based on the numerical solution method. Finally, the simulation approach is validated with measurements and shows good consistency. The simulation model is therefore capable of predicting transient gear contact under different operating conditions such as load vibrations or gear rattling. Simulations of complete transmissions are possible and therefore a direct determination of transmission vibration behavior and structure-borne noise as well as of forces and lubrication conditions can be done.

Efficient Transient Simulation of Non-linear Dynamic Networks with Discontinuous Forcing

AbstractNew technologies produce highly complex hybrid systems containing analogue components next to digital hardware and software. Simulating those mixed-signal systems exhibits discontinuities in signals due to the nature of the digital components. In this paper, an efficient and accurate method for the transient analysis of non-linear dynamic systems is presented that can handle discontinuous forcing functions which may occur as prescribed voltages or forces, for instance. It is based on a transformation of a model's equation system by substituting the time for a new independent variable. This approach facilitates suitable system-level models that altogether maintain the performance that is needed for an overall system-level simulation of complex application scenarios.

Transient flow simulation of municipal gas pipelines and networks using semi implicit finite volume method

An efficient transient flow simulation for gas pipelines and networks is performed. The proposed transient flow simulation is based on the transfer function models and finite volume method. The equivalent transfer functions of the nonlinear governing equations are derived for different boundary condition types. To verify the accuracy of the proposed simulation, the results obtained are compared with those of the experiments. The effect of the flow inertia is considered in this simulation with discretisation by TVD scheme. The accuracy of the proposed method is discussed for two test cases. It is shown that the proposed simulation has a sufficient accuracy.

The accuracy and efficiency of a MATLAB-Simulink library for transient flow simulation of gas pipelines and networks

An efficient transient flow simulation for gas pipelines and networks is proposed. The proposed transient flow simulation is based on the transfer function models and MATLAB-Simulink. The equivalent transfer functions of the nonlinear governing equations are derived for different boundary conditions types. Next, a MATLAB-Simulink library is developed and proposed considering any boundary condition. To verify the accuracy and the computational efficiency of the proposed simulation, the results obtained are compared with those of the conventional finite difference schemes (such as total variation diminishing algorithms, method of lines, and other finite difference implicit and explicit schemes). The effect of the flow inertia is incorporated in this simulation. The accuracy and computational efficiency of the proposed method are discussed for several test cases. It is shown that the proposed simulation has a sufficient accuracy and it is computationally more efficient than the other methods.