A semi-analytic boundary element method for parabolic problems

A new semi-analytic solution method is proposed for solving linear parabolic problems using the boundary element method. This method constructs a solution as an eigenfunction expansion using separation of variables. The eigenfunctions are determined using the dual reciprocity boundary element method. This separation of variables-dual reciprocity method (SOV-DRM) allows a solution to be determined without requiring either time-stepping or domain discretisation. The accuracy and computational efficiency of the SOV-DRM is found to improve as time increases. These properties make the SOV-DRM an attractive technique for solving parabolic problems.     

Robust actuator fault isolation and management in constrained uncertain parabolic PDE systems

This paper presents a methodology for the design of an integrated robust fault detection and isolation (FDI) and fault-tolerant control (FTC) architecture for distributed parameter systems modeled by nonlinear parabolic Partial Differential Equations (PDEs) with time-varying uncertain variables, actuator constraints and faults. The design is based on an approximate finite-dimensional system that captures the dominant dynamics of the PDE system. Initially, an invertible coordinate transformation-obtained through judicious actuator placement-is used to transform the approximate system into a form where the evolution of each state is excited directly by only one actuator. For each state, a robustly stabilizing bounded feedback controller that achieves an arbitrary degree of asymptotic attenuation of the effect of uncertainty is then synthesized and its constrained stability region is explicitly characterized in terms of the constraints, the actuator locations and the size of the uncertainty. A key idea in the controller synthesis is to shape the fault-free closed-loop response of each state in a prescribed fashion that facilitates the derivation of (1) dedicated FDI residuals and thresholds for each actuator, and (2) an explicit characterization of the state-space regions where FDI can be performed under uncertainty and constraints. A switching law is then derived to orchestrate actuator reconfiguration in a way that preserves robust closed-loop stability following FDI. Precise FDI rules and control reconfiguration criteria that account for model reduction errors are derived for the implementation of the FDI-FTC structure on the distributed parameter system. Finally, the results are demonstrated using a tubular reactor example.     

On sparse lu factorization procedures for the solution of parabolic differential equations in three space dimensions

The numerical solution of partial differential equations in 3 dimensions by finite difference methods leads to the problem of solving large order sparse structured linear systems.

In this paper, a factorization procedure in algorithmic form is derived yielding direct and iterative methods of solution of some interesting boundary value problems in physics and engineering.     

Unconditionally stable C1-cubic spline collocation method for solving parabolic equations

This article aims to present a new approach based on C¹-cubic splines introduced by Sallam and Naim Anwar [Sallam, S. and Naim Anwar, M. (2000). Stabilized cubic C¹-spline collocation method for solving first-order ordinary initial value problems, Int. J. Comput. Math., 74, 87–96.], which is A-stable, for the time integration of parabolic equations (diffusion or heat equation). The introduced method is an example of the so-called method of lines (the solution is thought to consist of space discretization and time integration), which is an extension of the 1/3-Simpson's finite-difference scheme. Our main objective is to prove the unconditional stability of the proposed method as well as to show that the method is convergent and is of order O (h ²)?+?O (k ⁴) i.e. it is a fourth-order in time and second-order in space. Computational results also show that the method is relevant for long time interval problems.     

Analysis of Rim Supports for Off‐Axis Inflatable Reflectors. I: Loads

A structural analysis is performed for the rim support of a pressurized off‐axis paraboloidal membrane, serving as a space‐based solar concentrator. The function of the rim support is to take up the tensile forces created by the stretched membrane. This paper deals with the load analysis. The tensile forces transmitted by the membrane to the rim support are calculated, and are proportional to pb, where p is the inflation pressure and b is one‐half the major axis of the elliptical rim. Next, the internal forces and moments generated in the rim support by the membrane forces are calculated. The compression forces are considerably larger, at any point, than the shear forces; both are proportional to pb2. The bending moments are proportional to pb3. The critical point is found to be at the top of the rim, where both the bending moment and compression force are at their maximum.     

Techno-economic study of hydrogen production using CSP technology

There are different processes for hydrogen production and different sources of energy could be used to drive these processes. However, a hydrogen production technique won't insure market penetration unless it succeeds in securing the economic competitiveness.In the present work, techno-economic study of the solar-electrolysis based hydrogen production techniques is carried out. The present study is limited to the case of hydrogen production using a hybrid solar parabolic trough-gas power plant-electrolysis system. The effect on hydrogen production cost of different factors, such the direct normal irradiance and the solar fraction are investigated.This technique of hydrogen production is considered for the case of Algeria. In order to determine the effect of the climatic conditions on the cost of hydrogen production, two different sites have been chosen: one in Northern Algeria and the other one in Southern Algeria.The results indicate that the cost of hydrogen production is dominated by the cost of hydrogen related to the cost of energy production. This cost is highly dependent on solar fraction and solar insolation. The results show also that solar CSP based hydrogen production technique is more competitive than the conventional PV based hydrogen production technique but as competitive or less competitive than CPV based hydrogen production technique.     

Dynamic modelling of a low-concentration solar power plant: A control strategy to improve flexibility

This paper deals with a dynamic analysis on a low concentration solar power plants coupled with Organic Rankine Cycles (ORC), which can be an alternative to PV systems because of their capability of providing a smoother electricity production due to their thermal inertia. At least within certain restraints, moreover they are able to exploit diffused solar radiation.The dynamic model of a plant with static Compound Parabolic Collectors and an ORC system, using a rotary volumetric expander, was developed using the simulation tool AMESim. All the main components of the plant are modelled: solar collectors field, heat transfer fluid circuit, heat exchangers and the ORC system. The plant response to the radiation of different days was analyzed to quantify the daily production and the trend of various plant parameters. Real ambient conditions were employed for the simulations by using data obtained by historical series.The results showed that the employment of a volumetric expansion device with variable rotating speed allows the plant to operate at different radiations and ambient temperatures without the need of any storage system or external heat sources. Results can be extended to other applications, such as low temperature waste heat recovery or geothermal systems.     

Explicit solution for normal depth of parabolic section of open channels

To obtain the normal depth of parabolic section of open channels, multiple known parameters were incorporated into a comprehensive one by transforming basic equations, and a concept of the non-dimensional normal depth was introduced. The normal depth equations were simplified into a non-dimensional iterative formula that was proved to have a high velocity of convergence. By analyzing the comprehensive parameter and dimensionless normal depth under condition of usually adopted sizes of parabolic channels and through establishing their relationship, the iterative initial value of normal depth was obtained. The normal depth of parabolic channels was acquired by substituting the initial value into the iteration formula. The error analysis was made and a case study was provided as an application example. The case study showed that the iteration formula was very simple, convenient and precise for determining the normal depth of parabolic channels with the maximum relative error of normal depth being less than 0.34% when the ratio of width to depth was between 0.2 and 20.     

求解抛物型方程的两层高精度差分格式

抛物型偏微分方程在工程技术与自然科学领域中扮演着重要作用,特别是在渗流、热传导、扩散等领域.对抛物型方程进行数值解法研究,在网格剖分的基础上,先给出一个含参数的差分格式,利用泰勒级数展开法和待定系数法使该差分格式的截断误差达到O(τ3+h5),通过方程组确定参数,得到一个两层高精度差分格式;然后用Fourier 分析法...