ROMB IMPLICIT FINITE-VOLUME METHOD TO SOLVE 2D HYDRODYNAMIC EQUATIONS ON UNREGULAR TRI- AND QUADRANGULAR GRIDS
E. M. Vaziev, A. D. Gadzhiev, S. Yu. Kuzmin
VANT. Ser.: Mat. Mod. Fiz. Proc 2006. Вып.4. С. 15-28.
We studied the implicit finite-volume method ROMB to solve 2D hydrodynamic equations on unregular tri- and quadrangular grids. The uniform grid can be used as a particular case. The investigated method is based on Lagrangian-Euler medium description with the implemented method of concentrations, grid remapping and recalculation of values using fractional design style. The state vector  is stored at cell centers and the coordinates  — at cell nodes. The difference scheme is based on the integral laws of conservation of mass, momentum and energy for cell; this makes the scheme conservative. The way of artificial dissipation introduction is one of the scheme characteristics. It is introduced in the equation of motion, as well as in the equation for pressure by the dissipation quantities  , related to  , as  grad P. ROMB method in conjunction with other scheme characteristics demonstrates better monotony as compared with traditional schemes with diversity model, which appeared to be especially important for unregular grids.
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