SPLITTING ALGORITHMS FOR NUMERICAL SOLUTION OF NAVIER — STOKES EQUATIONS IN FLUID DYNAMICS PROBLEMS

Journal of Applied Mechanics and Technical Physics - Implicit finite-volume predictor-corrector algorithms based on the splitting method are proposed for the numerical solution of the...     

Numerical Simulation of Plasma Dynamics in a Nonuniform Magnetic Field

An efficient algorithm is proposed enabling numerical simulations of plasma dynamics in a nonuniform magnetic field. The present numerical data are in good agreement with experimental data obtained in a GOL-3 setup and with previous simulations. The experimentally observed effect of fast transfer of energy to ions is confirmed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 35–45, January–February, 2006.     

Simulation of the motion and heating of an irregular plasma

A physicomathematical model for plasma heating and confinement is formulated on the basis of some assumptions on the behavior of a dense plasma cloud in a magnetic field. The model allows for the ionization and heating of the plasma cloud by the surrounding deuterium plasma due to heat conduction and heating by a superthermal electron current. The expansion of a plasma cloud in an external magnetic field is studied using some simplifications in a magnetohydrodynamic approximation. Plasma heating is modeled by an external source. The basic equations include continuity, motion, energy, and magneticfield equations. For numerical solution of the problem, we developed a finitedifference scheme of the type of a universal algorithm with splitting into physical processes and spatial directions, which allowed us to obtain separate solutions of the equations of magnetic induction and gas dynamics. Calculations of the propagation of a plasma cloud heated by a source in an external magnetic field were performed. The mechanism of the effect of the magnetic field and heat source on plasma cloud expansion is determined. The results agree qualitatively with experimental data.     

Numerical simulation of plasma motion in a magnetic field. Two-dimensional case

A model of dynamics and heating of a plasma cloud in a magnetic field is considered in a two-temperature approximation. Based on a predictor-corrector-type implicit difference scheme, spreading of a plasma cloud in an external magnetic field is numerically simulated, and the influence of this field on spread dynamics is evaluated. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 121–132, May–June, 2007.     

A factorization method for numerical solution of the Navier–Stokes equations for a viscous incompressible liquid

Some implicit difference scheme of approximate factorization is proposed for numerical solution of the Navier–Stokes equations for an incompressible liquid in curvilinear coordinates. Testing of the algorithm is carried out on the solution of the problems concerning the Couette and Poiseuille flows; and the results are presented of numerical simulation of a flow between the rotating cylinders with covers.     

Simulation of supersonic flows on the basis of splitting algorithms

For the numerical simulation of aerodynamics problems, the Euler and Navier — Stokes equations written in integral form are used to construct an implicit finite-volume predictor-corrector scheme. At the predictor stage, the splitting of equations into physical processes and spatial directions is introduced, which makes it possible to reduce the solution of the original system to the solution of individual equations on fractional steps by the scalar sweep method and ensure the stability of the algorithm as a whole. The paper also describes the supersonic gas flows in a narrowing channel with regular and non-regular reflection of the compression shock from the symmetry plane and the numerical substantiation of the existence of pulsating flow with a supersonic flow past a cylinder with a needle.     

Application of Splitting Algorithms in the Method of Finite Volumes for Numerical Solution of the Navier–Stokes Equations

We generalize the splitting algorithms proposed earlier for the construction of efficient difference schemes to the finite volume method. For numerical solution of the Euler and Navier–Stokes equations written in integral form, some implicit finite-volume predictor-corrector scheme of the second order of approximation is proposed. At the predictor stage, the introduction of various forms of splitting is considered, which makes it possible to reduce the solution of the original system to separate solution of individual equations at fractional steps and to ensure some stability margin of the algorithm as a whole. The algorithm of splitting with respect to physical processes and spatial directions is numerically tested. The properties of the algorithm are under study and we proved its effectiveness for solving two-dimensional and three-dimensional flow-around problems.