THE IMPLICIT FINITE-DIFFERENCE METHOD ROMB FOR SOLVING 2D GAS-DYNAMIC EQUATIONS
A.D. Gadzhiev, S.Yu. Kuzmin, S.N. Lebedev, V.N. Pisarev
VANT. Ser.: Mat. Mod. Fiz. Proc 2001. Вып.4. С. 11-21.
The implicit finite-difference method ROMB for numerical solution of 2D gas-dynamic equations is presented. The method is based on the use of arbitrary Lagrangian-Eulerian quadrangle grids. The scheme is unconditionally stable and allows simulating the currents of both almost non compressible and strong compressible medium. The "diamond" approximations are simple and provide the satisfactory accuracy for highly deformed non-orthogonal grids. The scheme of the ROMB technique is conservative (a complete conservatism easy to achieve with respect) to energy equation. For 2D difference equations system solution the economical iterative method with stabilizing correction is used. The examples of calculations are given.
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