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Since 1978
Published in Sarov (Arzamas-16), Nizhegorodskaya oblast |
RUSSIAN FEDERAL
NUCLEAR CENTER -
ALL-RUSSIAN RESEARCH INSTITUTE
OF EXPERIMENTAL PHYSICS |
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 Русский |  English
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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.
| THE STUDY OF ROMB SCHEME FOR SOLVING 2D GAS-DYNAMIC EQUATIONS WITH THE METHOD OF APRIORI ESTIMATES
A.D. Gadzhiev, S.Yu. Kuzmin
VANT. Ser.: Mat. Mod. Fiz. Proc 2001. Вып.4. С. 22-29.
A theoretical investigation of the implicit finite-difference method ROMB for numerical solution of gas-dynamic equations is carried out. A study is made of an approximation error which turns out to be the error of the second order of smallness, both on irregular and non-orthogonal grids. The scheme steadiness for initial data, right side and boundary conditions is proved by the method of energetic inequalities. A proof is given for the method convergence in a form of apriori estimates.
| TOM4-KD TECHNIQUE FOR COMPUTATIONAL SIMULATING 2D EQUATIONS OF RADIATION TRANSFER IN MULTI-GROUP QUASI-DIFFUSIVE APPROXIMATION
A.D. Gadzhiev, E.M. Romanova, V.N. Seleznev, A.A. Shestakov
VANT. Ser.: Mat. Mod. Fiz. Proc 2001. Вып.4. С. 48-59.
The solution of 2D equations of radiation transfer in multi-group quasi-diffusive approximation with the difference scheme ROMB is considered. P1-corrections method is used to accelerate iterations when solving the system of quasi-diffusive equations. Correction equations are solved by a diagonal element selection method.
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