The Boundary Element Method for the Solution of the Backward Heat Conduction Equation

1995 ◽  
Vol 116 (2) ◽  
pp. 292-299 ◽  
Author(s):  
H. Han ◽  
D.B. Ingham ◽  
Y. Yuan
Keyword(s):  
Heat Conduction ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Element Method

Mould cooling simulation for injection moulding using a fast boundary element method approach

2009 ◽  
Vol 224 (4) ◽  
pp. 653-662 ◽  
Author(s):  
H Zhou ◽  
Y Zhang ◽  
J Wen ◽  
S Cui
Keyword(s):  
Heat Conduction ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Injection Moulding ◽  
Heat Conduction Problem ◽  
Solution Time ◽  
Combination Method ◽  
Dynamic Allocation ◽  
Actual Problem ◽  
Element Method

The existing cooling simulations for injection moulding are mostly based on the boundary element method (BEM). In this paper, a fast BEM approach for mould cooling analysis is developed. The actual problem is decoupled into a one-dimensional transient heat conduction problem within the thin part and a cycle-averaged steady state three-dimensional heat conduction problem of the mould. The BEM is formulated for the solution of the mould heat transfer problem. A dynamic allocation strategy of integral points is proposed when using the Gaussian integral formula to generate the BEM matrix. Considering that the full and unsymmetrical influence matrix of the BEM may lead to great storage space and solution time, this matrix is transformed into a sparse matrix by two methods: the direct rounding method or the combination method. This approximated sparsification approach can reduce the storage memory and solution time significantly. For validation, six typical cases with different element numbers are presented. The results show that the error of the direct rounding method is too large while that of the combination method is acceptable.

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