Modified Method of Characteristics for Simulating Microscale Energy Transport

2004 ◽  
Vol 126 (5) ◽  
pp. 735-743 ◽  
Author(s):  
Laurent Pilon ◽  
Kamal M. Katika
Keyword(s):  
Steady State ◽  
Numerical Scheme ◽  
Method Of Characteristics ◽  
Energy Transport ◽  
Numerical Solutions ◽  
Computational Cost ◽  
Phonon Transport ◽  
Coupled Equations ◽  
Heat Carriers ◽  
Transient And Steady State

This paper presents a new numerical scheme for simulating multidimensional transient and steady-state microscale energy transport. The new method is based on the method of characteristics that follows heat carriers along their pathline. Unlike traditional methods, it uses a fixed computational grid and follows the heat carriers backward in time. The method 1) is accurate, 2) is unconditionally stable, 3) can deal with complex geometries without a large increase in computational cost, and 4) can be used for solving coupled equations using other numerical schemes. First, the numerical scheme is described. Then, simulations for transient and steady-state phonon transport in dielectric thin films are discussed. Numerical results are compared with analytical and reported numerical solutions and good agreement is obtained.

scholarly journals Neural network–based nonaffine control of air-breathing hypersonic vehicles with prescribed performance

2018 ◽  
Vol 15 (1) ◽  
pp. 172988141875524 ◽  
Author(s):  
Xiangwei Bu ◽  
Qing Wang
Keyword(s):  
Steady State ◽  
Neural Control ◽  
Tracking Error ◽  
Computational Cost ◽  
Design Procedure ◽  
Hypersonic Vehicles ◽  
Tracking Errors ◽  
Air Breathing ◽  
Prescribed Performance ◽  
Transient And Steady State

This article investigates a novel nonaffine control strategy using neural networks for an air-breathing hypersonic vehicle. Actual actuators are regarded as additional state variables and virtual control inputs are derived from low-computational cost neural approximations, while a new altitude control design independent of affine models is addressed for air-breathing hypersonic vehicles. To further reduce the computational load, an advanced regulation algorithm is applied to devise adaptive laws for neural estimations. Moreover, a new prescribed performance mechanism is exploited, which imposes preselected bounds on the transient and steady-state tracking error performance via developing new performance functions, capable of guaranteeing altitude and velocity tracking errors with small overshoots. Unlike some existing neural control methodologies, the proposed prescribed performance-based nonaffine control approach can ensure tracking errors with preselected transient and steady-state performance. Meanwhile, the complex design procedure of backstepping is also avoided. Finally, simulation results are presented to validate the design.

Modeling of assembly systems with complex structures for throughput analysis during transients

2019 ◽  
Vol 39 (2) ◽  
pp. 262-271
Author(s):  
Yukan Hou ◽  
Yuan Li ◽  
Yuntian Ge ◽  
Jie Zhang ◽  
Shoushan Jiang
Keyword(s):  
Steady State ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Assembly Systems ◽  
Complex Structures ◽  
Throughput Performance ◽  
Throughput Analysis ◽  
Content Type ◽  
Serial Production Lines ◽  
Transient And Steady State

Purpose The purpose of this paper is to present an analytical method for throughput analysis of assembly systems with complex structures during transients. Design/methodology/approach Among the existing studies on the performance evaluation of assembly systems, most focus on the system performance in steady state. Inspired by the transient analysis of serial production lines, the state transition matrix is derived considering the characteristics of merging structure in assembly systems. The system behavior during transients is described by an ergodic Markov chain, with the states being the occupancy of all buffers. The dynamic model for the throughput analysis is solved using the fixed-point theory. Findings This method can be used to predict and evaluate the throughput performance of assembly systems in both transient and steady state. By comparing the model calculation results with the simulation results, this method is proved to be accurate. Originality/value This proposed modeling method can depict the throughput performance of assembly systems in both transient and steady state, whereas most exiting methods can be used for only steady-state analysis. In addition, this method shows the potential for the analysis of complex structured assembly systems owing to the low computational complexity.

Non-symmetric flow in Laval type nozzles

1972 ◽  
Vol 273 (1232) ◽  
pp. 185-235 ◽  
Keyword(s):  
Steady State ◽  
Combustion Chamber ◽  
Method Of Characteristics ◽  
Three Dimensions ◽  
Symmetric Flow ◽  
Gaseous Flow ◽  
The Method Of Characteristics ◽  
Lateral Forces

The equations of the steady state, compressible inviscid gaseous flow are linearized in a form suitable for application to nozzles of the Laval type. The procedure in the supersonic phase is verified by comparing solutions so obtained with those derived by the method of characteristics in two and three dimensions. Likewise, the solutions in the transonic phase are com pared with those obtained by other investigators. The linearized equation is then used to investigate the nat re of non-symmetric flow in rocket nozzles. It is found that if the flow from the combustion chamber into the nozzle is non-symmetric, the magnitude and direction of the turning couple produced by the emergent jet is dependent on the profile of the nozzle and it is possible to design profiles such that the turning couples or lateral forces are zero. The optimum nozzle so designed is independent of the pressure and also of the magnitude of the non-symmetry of the entry flow. The formulae by which they are obtained have been checked by extensive static and projection tests with simulated rocket test vehicles which are described in this paper.

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