非定常熱伝導問題の数値解法に関する一考察

概要

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Unsteady thermal conduction problems in the form of ∂φ/∂θ=α∇2φ were numerically solved under the Dirichlet condition, by using the explicit finite difference method, and the effect of initial boundary value on the predicted results was studied. 1-dimensional problem was solved by using the scheme; φp, r+1=1/6 [(+1)-(+4)-(+1)] φp, r where subscript “p” denotes the spatial point and “r” the time step. For 2-dimensional problem, the analysis was based on a new scheme : φp, q, r+1=1/36 [(+1)-(+4)-(+1)-(+4)-(+16)-(+4)-(+1)-(+4)-(+1)] φp, q, r The choice of initial boundary values, φ0, 0 (=φN, 0) for 1-dimensional andφ0, q, 0 (φp, 0, 0=φN, q, 0=φp, N, 0) for 2-dimensional, was of importance, especially for the initial stage, in view of the accuracy of the results.By taking this into account, the same optimal value of 0.5 was found for both 1-dimensional and 2-dimensional problems.
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