MIXED CELLS COMPUTATION WITH 2-D "D" CODES

V.I. Budnikov, V.B. Vershinin, V.I. Delov, V.V. Sadchikov, E.S. Khiteva, Yu.D. Chernyshev
VANT. Ser.: Mat. Mod. Fiz. Proc. 2001. No 3. P. 3-13.

The paper presents the method for defining mixed cells in D complex and studies two models for computing gas-dynamic and elastic-plastic values in mixed cells. The algorithms for selecting substance separation boundaries in mixed cells and results of problems test computations using mixed cells in D complex are given.

P.A. Avdeev, M.V. Artamonov, S.M. Bakhrakh, S.V. Velichko, N.A. Volodina, N.M. Vorob'eva, S.P. Egorshin, E.N. Esaeva, A.D. Kovaleva, M.V. Luchinin, S.N. Pronevich, V.F. Spiridonov, I.Yu. Taraday, A.N. Tarasova, E.V. Shuvalova
VANT. Ser.: Mat. Mod. Fiz. Proc. 2001. No 3. P. 14-18.

The paper describes fundamentals of the method implemented in the program complex LEGAK intended for time-dependent multi-constituent continuum flow computations.
The principles of LEGAK program complex parallelization using multiprocessor distributed-memory computers are discussed.
    LEGAK implementation on multiprocessor computer systems allowed computations with a significantly larger number of computational points than using non-scalar computers which is of especial importance when numerically simulating contact boundary instabilities.

A.B. Mazo
VANT. Ser.: Mat. Mod. Fiz. Proc. 2001. No 3. P. 19-25.

A technique for computing thermodynamic fields in two- or three-phase systems with phase transition of water on the surface of drops, films and canal walls is proposed. A study is made of two model problems on evaporation of falling drops in upward air current and on moisture condensation from vapour-gas mixture and ice coat formation on a cooled canal wall.

V.E. Shemarulin
VANT. Ser.: Mat. Mod. Fiz. Proc. 2001. No 3. P. 26-36.

The author gives an explicit description of the structure of 3-D stationary (with rank 1) and 2-D time-dependent isobar (inertial) flows of an ideal incompressible liquid. It is shown that all such flows (both 3-D and 2-D) form a union of flow areas of three main types - shearing, conical and tangential. Time-dependent flows in R²(x,y) therewith are considered to be stationary ''flows" in R³(x,y,t). Specific examples of conical flows are given.

V.M. Konyukhov, A.N. Chekalin
VANT. Ser.: Mat. Mod. Fiz. Proc. 2001. No 3. P. 37-48.

The authors have developed a two-level mathematical model of timedependent processes of oil recovery under water drive in a seamy-porous pool, formed with blocks, surrounded by cracks. The processes in the cracks (outer level) are described by the equations of two-phase filtration with regard to elasticity capacity of cracks and fluids with linear saturation dependence of phase permeabilities. Mass sources, included into these equations, are integral characteristics of the problem solution for blocks (inner level). The process of two-phase filtration is considered in each individual block. The blocks have their own coordinate system; coordinates of an outer problem act as parameters of an inner problem. The equations of two-phase filtration with regard to elasticity capacity of porous medium and phases with cubic saturation dependence of relative phase permeabilities are used for describing processes in blocks. In these equations source terms are absent, as mass transfer between a crack and a block goes on through the block boundary.
    A difference scheme for solving these interrelated problems is presented; numerical methods and algorithms are described. The results of computational experiments on studying oil recovery mechanism and iterative effect on seamy-porous pool are given.

V.I. Budnikov, V.I. Delov, O.K. Loginova
VANT. Ser.: Mat. Mod. Fiz. Proc. 2001. No 3. P. 49-59.

The paper describes a technique for automatic determination of the situation, when a global correction of 2-D Lagrangian grid is required. Criteria and algorithms are given to select optimal neighborhood of bad grid nodes, where the grid is

V.F. Kuropatenko, I.I. Kuznetsova, I.R. Makeeva, A.S. Murashko, V.N. Uvarov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2001. No 3. P. 60-71.

The paper considers the problem on effect of cyclic air injection through a narrow slot located at a streamlined body on a flow characteristics. The air moves through the slot in such a way that injection alternate with suction. Two new difference schemes were used to solve the problem. The flow was computed in two dimensions. The characteristics of difference schemes are discussed, including monotonicity, energy dissipation and discontinuities destraction.

S.M. Bakhrakh, S.V. Mikhaylov, A.O. Naumov, V.F. Spiridonov, E.V. Shuvalova
VANT. Ser.: Mat. Mod. Fiz. Proc. 2001. No 3. P. 72-79.

The paper deals with the matters centred around constructing difference scheme to solve an equation of motion at calculating time-dependant elastic-plastic flows. The difference scheme, which determines accelerations on the computational cell sides and interpolates them on the cell nodes is introduced into LEGAK complex.
    A new and an old difference schemes are compared on test computations.
    The advantages of the new scheme have shown themselves in computing material destruction according to a binary test accounting for both tensions and shearing strains.