On preconditioned BiCGSTAB solver for MLPG method applied to heat conduction in 3D complex geometry

2018 ◽  
Vol 93 ◽  
pp. 83-93 ◽  
Author(s):  
Rituraj Singh ◽  
Krishna Mohan Singh
2019 ◽  
Vol 36 (4) ◽  
pp. 1323-1345
Author(s):  
Rituraj Singh ◽  
Krishna Mohan Singh

Purpose The purpose of this paper is to assess the performance of the stabilised moving least squares (MLS) scheme in the meshless local Petrov–Galerkin (MLPG) method for heat conduction method. Design/methodology/approach In the current work, the authors extend the stabilised MLS approach to the MLPG method for heat conduction problem. Its performance has been compared with the MLPG method based on the standard MLS and local coordinate MLS. The patch tests of MLS and modified MLS schemes have been presented along with the one- and two-dimensional examples for MLPG method of the heat conduction problem. Findings In the stabilised MLS, the condition number of moment matrix is independent of the nodal spacing and it is nearly constant in the global domain for all grid sizes. The shifted polynomials based MLS and stabilised MLS approaches are more robust than the standard MLS scheme in the MLPG method analysis of heat conduction problems. Originality/value The MLPG method based on the stabilised MLS scheme.


Author(s):  
Nam-il Tak ◽  
Min-Hwan Kim ◽  
Hong-Sik Lim ◽  
Goon-Cherl Park

The recent rapid development of computational fluid dynamics (CFD) technology provides a powerful tool to obtain accurate temperature distribution of prismatic fuel blocks. In general, however, a CFD analysis requires tremendous computational efforts to analyze whole prismatic fuel blocks due to complex geometry and near wall treatment to resolve the boundary layer of the fluid flow. Such efforts might be a huge burden for a designer who wants a large number of calculations with various design options. Recently, a practical method to analyze a thermal behavior of prismatic fuel blocks has been developed by the present authors to overcome the demerits of CFD and system code calculations. The developed method solves three-dimensional heat conduction in prismatic fuel blocks like a CFD code. For the fluid, however, the present method adopts one-dimensional conservation equations like a system code. Such a combination enables significantly reduced computational effort with reasonable computational accuracy. This paper presents an intensive thermo-fluid analysis for prismatic fuel assemblies using the new method. In order to examine the validity and the accuracy of the developed method, at first, single standard and control fuel assemblies have been analyzed and compared with the CFD results. Then the developed method has been applied to a whole core thermal analysis of a prismatic reactor.


2013 ◽  
Vol 465-466 ◽  
pp. 490-495 ◽  
Author(s):  
Mas Irfan P. Hidayat ◽  
Bambang Ari-Wahjoedi ◽  
Parman Setyamartana ◽  
Puteri S.M. Megat Yusoff ◽  
T.V.V.L.N. Rao

In this paper, a new meshless local B-spline basis functions-finite difference (FD) method is presented for two-dimensional heat conduction problem with spatially varying heat generation. In the method, governing equations are discretized by B-spline approximation in the spirit of FD technique using local B-spline collocation. The key aspect of the method is that any derivative at a point or node is stated as neighbouring nodal values based on the B-spline interpolants. Compared with mesh-based method such as FEM the method is simple and efficient to program. In addition, as the method poses the Kronecker delta property, the imposition of boundary conditions is also easy and straightforward. Moreover, it poses no difficulties in dealing with arbitrary complex domains. Heat conduction problem in complex geometry is presented to demonstrate the accuracy and efficiency of the present method.


Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3319-3337
Author(s):  
Akbar Karami ◽  
Saeid Abbasbandy ◽  
Elyas Shivanian

In this paper we investigated the inverse problem of identifying an unknown time-dependent coefficient and free boundary in heat conduction equation. By using the change of variable we reduced the free boundary problem into a fixed boundary problem. In direct solver problem we employed the meshless local Petrov-Galerkin (MLPG) method based on the moving least squares (MLS) approximation. Inverse reduced problem with fixed boundary is nonlinear and we formulated it as a nonlinear least-squares minimization of a scalar objective function. Minimization is performed by using of f mincon routine from MATLoptimization toolbox accomplished with the Interior - point algorithm. In order to deal with the time derivatives, a two-step time discretization method is used. It is shown that the proposed method is accurate and stable even under a large measurement noise through several numerical experiments.


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