| Abstrakt: |
This paper presents a numerical study of the convergence order of the projection-characteristic of the cubic polynomial projection (СРР) method for solving a three-dimensional stationary transport equation on unstructured tetrahedral meshes. The method is based on a characteristic approach to solve the transport equation, has a minimal stencil within a single tetrahedron, and a high (third) order of approximation. Unlike classical grid-characteristic methods, in this method, the final numerical approach is constructed based not on the interpolation operators of some order of approximation but on the orthogonal projection operators on the functional space used to approximate the solution. The base scheme is a one-dimensional scheme referred to as the Hermitian cubic interpolation (СIP) scheme. The use of interpolation operators is often designed to be applied to sufficiently smooth functions. However, even if the exact solution has sufficient smoothness, some types of tetrahedra illumination lead to the appearance of nonsmooth grid solutions. The transition to orthogonal projectors solves two problems: firstly, the problem of the appearance of angular directions that are coplanar with the faces of the cells, and secondly, the problem of the appearance of nonsmooth numerical solutions in the faces of the mesh cell. The convergence result is compared with the theoretical estimates obtained for the first time by one of the authors of this study. The third order of convergence of the method is shown, provided that the solution is sufficiently smooth and the absorption coefficient in the cells is close to constant. [ABSTRACT FROM AUTHOR] |
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