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THE ADAPTIVE METHOD FOR SOLVING A MULTIDIMENSIONAL TRANSPORT EQUATION USING REFINED GRIDS IN PHASE SPACE

R. M. Shagaliev
VANT. Ser.: Mat. Mod. Fiz. Proc 2004. Вып.4. С. 3-15.

The paper offers the approach to multidimensional transport equation approximation with introduction of adaptive built-in refined grids in phase space. The adaptive method is formulated for the general case of using arbitrary non-orthogonal spatial grids. In 2D problems, the grids in use are either regular non-orthogonal quadrangular, or irregular grids of convex polygons. The mathematical principles of the adaptive method for refined grids have been formulated. Since the problem of approximating the transport equation in phase space using refined grids in angular variables is the most hard to solve, the detailed description of the development of algorithms and difference equations of the adaptive method for such the case is given.



NUMERICAL SOLVING THE 2D TRANSPORT EQUATION BY USING THE ADAPTIVE-BY-SPACE METHOD OF FRACTIONAL GRIDS

R. M. Shagaliev, A. V. Alekseev, I. M. Belyakov, A. V. Gichuk, V. V. Evdokimov, A. N. Moskvin, A. A. Nuzhdin, N. P. Pleteneva, T. V. Shemyakina
VANT. Ser.: Mat. Mod. Fiz. Proc 2004. Вып.4. С. 16-26.

The adaptive-by-space-variables algorithm of grid fractioning, used at numerical solving 2D transport equation, is described in the paper. The results of numerical research of this method, conducted on the example of radiation spread problem computation, are presented. The results obtained by using the adaptive methods, were compared to those, obtained by using standard scheme without adaptivity. For both computations the computation time was determined. The computation time gain, comparing to the standard method, at obtaining approximately the same accuracy of the result, was taken as the adaptive method efficiency criterion.










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