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A Tensor Transformation Technique for the Transport Equation

S. L. Gralnick

Nuclear Science and Engineering

Volume 59 / Number 4 / April 1976 / Pages 311-318


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A step-wise tensor transformation technique is presented for the transformation of the single energy group transport equation to an arbitrary spatial coordinate system. Both gradient and divergence forms of the equation are given, and the same method is applied to the derivation of the diffusion approximation. We demonstrate that using an orthogonal representation of the propagation vector will simplify the divergence form of the equation. The application of this technique is in the representation of the transport equation in coordinate systems other than the usual rectangular, cylindrical, and spherical ones. Its use is demonstrated by transforming the transport equation to a toroidal coordinate system consisting of nested circular toroids.

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