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A high-order moc including a spatial polynomial expansion for cross sections

Abstract : The TDT (Two and Three Dimensional Transport) deterministic code of the APOLLO3 R calculation platform utilises the Method of Characteristics (MOC) to solve the Boltzmann equation for neutrons. In order to reduce the bias and the errors of the current schemes, in the recent years the TDT application has been extended to three-dimensional extruded geometries [1], to provide a better representation of 3D environment effects also in view of a future one-step core calculation. Even more recently, a polynomial description for the neutron flux has been introduced [2]: along the axial (extruded) direction a per-region constant (“step-constant”) flux representation has been substituted by a description assigning to each region a set of coefficients for the polynomial expansion. At the price of a greater complication in the equations, this has permitted to reduce the number of axial meshes by a factor higher than 10, the memory required by a factor ∼ 3 and the computation time by a factor ∼ 2. The present work constitutes the natural continuation of the one above, as the same treatment is given to both the neutron flux and the cross sections. The aim is to apply the polynomial expansion in the case of evolution calculations: as a matter of fact, the combination of a polynomial flux expansion and step-constant cross sections over extended axial meshes is highly inaccurate if non-zero burnup cases are considered, since a refined axial mesh is required to describe the modification of cross-section profiles due to nuclide depletion. A polynomial expansion for cross sections is therefore needed, together with the one for the flux, to fully utilize the MOC 3D polynomial method.
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A. Gammicchia, S. Santandrea, S. Dulla. A high-order moc including a spatial polynomial expansion for cross sections. ICTT - 2019 - 26th International Conference on Transport Theory, Sep 2019, Paris, France. ⟨cea-02973290⟩

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