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In this article, the application of discrete mollification as a regularization procedure for solving a nonlinear inverse problem in one dimensional space is considered. Illposedness is identified as one of the main characteristics of inverse problems. It is clear that if we have a noisy data, the inverse problem becomes unstable. As such, a numerical procedure based on discrete mollification and space marching method is applied to address the ill-posedness of the mentioned problem. The regularization parameter is selected by generalized cross validation (GCV) method. The numerical stability and convergence of the proposed method are investigated. Finally, some test problems, whose exact solutions are known, are solved using this method to show the effciency. [ABSTRACT FROM AUTHOR]

Highlights • An improved space marching method for nonlinear IHCP was proposed. • The number of future time steps was independent of space nodes. • Fully implicit scheme used so that algorithm is robust under various conditions. • Validation was conducted using numerical and experimental data. Abstract This paper presents an improved space marching technique for estimating the transient thermal boundary conditions including heat flux and temperature, based on the measured interior temperature history. The algorithm employs a fully implicit difference scheme thus is unconditionally stable for various space and time steps. In each space marching step, the number of used future temperatures can be randomly designated. The proposed method was tested with numerical and experimental data to verify its performances for both linear and nonlinear problems. Comparisons between the proposed method and the method of Raynaud and Bransier (1986) were also conducted using both the numerical and experimental data. In the testing with numerical data, the present method is better than the method of Raynaud and Bransier (1986) for small time steps where the estimating accuracy was dominated by the random error. In the testing with cryogenic quenching experimental data, it was found that the present method is applicable for processing temperature data involving local fluctuations and abrupt changes. By incorporating more future temperatures in each space marching step, the present method demonstrated a better performance in processing the experimental data. [ABSTRACT FROM AUTHOR]

A new modified space marching method is presented for solving transient nonlinear inverse heat conduction problems. The new method combines the merits of space marching and function specification methods. Future temperature measurements are used in a least square manner to stabilize the calculation results. The transient surface temperature and heat flux can be accurately recovered by the method without employing iteration procedure or data smoothing technique. Three types of heat flux profiles were used to evaluate the proposed inversion method and a comparison to the classical space marching method was drawn to demonstrate the advantage of the present method. A numerical experiment is performed to investigate the influence of parameters in the method as well as to illustrate the selection of optimal parameters. The present method calculates surface temperature and heat flux values in a sequential manner therefore is suitable for on-line estimation application. [ABSTRACT FROM AUTHOR]

A catalytic monolith converter usually comprise several hundred or thousands of channels. Mathematical modeling that seek to resolve the coupled transport phenomena – mass, momentum, species and heat – on a discrete-channel scale is a computationally-challenging task. In this context, we present an efficient approach to overcome the difficulties in the modeling of a monolith converter. In short, we establish the condition for validity of a fast and efficient reduced single monolith channel model for modeling multiple channels. The reduced model is then verified for an assembly of two channels with the full set of equations; good agreement is found for typical monolith material and operating conditions indicating the ability of the reduced model to capture conjugate heat transfer across channels. We then study the computational efficiency of the reduced model for monoliths comprising O (10 4 ) channels. The computational penalty for reduced model is much less as compared to the full model, making it a possible candidate for detailed monolith simulations. [ABSTRACT FROM AUTHOR]

A fast aerodynamic characteristics prediction technique is developed to predict aerodynamic force and heat, combining effective space marching numerical method with engineering method based on surface stream tracking technique. Hypersonic aerodynamic forces are obtained effectively by solving the Euler equations numerically with fast space marching method. In order to calculate the heat flux, an engineering method，called tracking the surface stream trace based on the axisymmetric analogue technique and boundary layer theory, is adopted and developed to be applicable for complex geometry. The inviscid flow parameters and surface stream lines required in the engineering method are obtained from above mentioned inviscous numerical flow fields. The proposed method for aerodynamic force and heat prediction is applied to high speed vehicles, the results show that the space marching method saves the computational cost enormously, approximately one order less comparing to the time marching method, while the two methods have similar precision in aerodynamic force evaluation. The predicted error of heat flux is within 20% comparing to that of wind tunnel test. The technique promoted is an effective approach suitable for the needs of fast aerodynamic configuration design and optimization. [ABSTRACT FROM AUTHOR]

In general, three-dimensional (3D) non-isothermal models for monolithic channels that seek to capture the local transport phenomena are computationally expensive. In this regard, we present a reduced model for a monolithic channel that reduces the computational cost, whilst preserving the 3D geometry and all of the essential physics – this is accomplished by exploiting the inherent slenderness of the monolith channel, coupled with scaling arguments, leading-order asymptotics and a fast space-marcher. The model takes into account conservation of mass, momentum, species and energy coupled with chemical kinetics, and is demonstrated for a three-way reaction mechanism for treatment of automotive exhaust. The results of the reduced model are verified against those of the full model and validated with axial temperature distributions for an experimental square channel. Overall, memory requirements and computing time are reduced by around 2–3 orders of magnitude as compared to the full set of equations. Finally, we discuss the suitability of the reduced model for reactor-scale modeling and extensions for transient simulations and other slender chemical engineering systems. [ABSTRACT FROM AUTHOR]

Aerodynamic configuration optimization study for a hypersonic vehicle is performed in the paper. In the optimization progress, a parameterized model is used and auto grids are achieved efficiently by solving parabolic equations. The aerodynamic force and heat are predicted by the technique which combined effective space marching numerical method and engineering method based on tracking the surface stream trace respectively. The aerodynamic characteristic of longitudinal static stability of the optimized shape is acquired through design optimization for high trimming angle of attack, and the maximum surface heat flux decreased 24% compared to the original shape. The technique promoted is an effective approach suitable for aerodynamic configuration preliminary designs of high speed vehicles. [ABSTRACT FROM AUTHOR]

Abstract: In general, detailed mechanistic models for fuel cell stacks that seek to capture the local transport phenomena are computationally expensive. In this context, we propose a hybrid modeling strategy, in which the steady-state conservation equations are solved iteratively in two separate groups: The first comprises asymptotically-reduced governing equations for momentum, mass, and species, which are solved as a transient-like propagation problem; the second comprises the full set of equations for energy and charge, which are solved as an elliptic stationary problem. Physically, the segregation is justified by the nature of the dependent variables; in essence, the first group covers local variables on the cell level and the second involves global variables on the stack level. We demonstrate the methodology for a steady-state detailed mechanistic model of a proton exchange membrane fuel cell stack comprising 2 to 350 cells subjected to non-uniform operating conditions across the cells; e.g., a stack comprising 350 cells takes less than an hour to solve. The proposed methodology is generic and can also be employed for other systems where transport phenomena occur on different length scales and involve some form of slenderness. [Copyright &y& Elsevier]

Abstract: 3D modeling for fuel cells is generally computationally expensive, especially for stacks. In order to reduce computational cost, spatial smoothing over the parallel plain channels in flow fields is introduced and applied to a 3D steady-state isothermal planar solid oxide fuel cell model, which is validated with experiment from literature. The 3D model is reduced to 2D coupled with effective parameters and correlation factors, and then asymptotically reduced to parabolic PDEs and ODEs associated with space marching. The correlation factors, which are derived based on a full set of governing equations for electrokenitics over a cell cross section, can handle not only variations in diffusion pathways due to ribs but also the coupling effect between governing equations. The reduced models are verified with the 3D counterpart in view of global and local properties. Good agreement with a quantitative loss of information is achieved. The reduction in computational cost is investigated. [Copyright &y& Elsevier]