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The Chinese also put a fictitious value on them.
We may derive such fictitious value of ∆εall by linear extrapolation of ∆ε from the positive to the negative temperature range (the result of the extrapolation is marked in Fig. 5 with dashed lines).
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Such an enforcement determines the fictitious values.
The concepts of primary and secondary fictitious values are introduced to deal with sharp-edged interfaces.
We propose secondary fictitious values and construct geometry based interpolation schemes to overcome this difficulty.
Interface jump conditions are enforced on the interface, which in turn, accurately determines fictitious values.
While a pair of fictitious values are determined along a mesh at a time, an iterative procedure is proposed to determine all the required fictitious values for higher-order schemes by repeatedly using the lowest order jump conditions.
In the proposed method, fictitious values are utilized so that the standard central finite different schemes can be employed regardless of the interface.
Fictitious values on the extended domains are determined by enforcing the physical jump conditions on the interface according to the local topology of the irregular point.
The proposed MIB method makes use of Cartesian grids, standard finite difference schemes, lowest order interface jump conditions and fictitious values.
The other is to make iterative use of only the lowest order jump conditions to determine the fictitious values on extended domains.
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