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FULLY CONSERVATIVE SPH-SYSTEMS IN GAS DYNAMICS AND A SCHEME FOR NUMERICALLY INTEGRATING THEM

I. D. Blazhnov, M. N. Vishnyakova, S. N. Polishchuk, B. P. Tikhomirov
VANT. Ser.: Mat. Mod. Fiz. Proc 2020. Вып.2. С. 16-32.

Fully conservative systems are identified among a set of ordinary differential equation systems of the smoothed particles hydrodynamics (SPH) method describing two-dimensional axially symmetric flows. A fully conservative SPH system has been constructed with the variational method and is a "duplicate" of the known Brookshaw system for equations in cylindrical coordinates. A modified predictor-corrector method for the numerical integration of SPH systems, which is based on the fully conservative central difference scheme of Lagrangian fluid dynamics, is proposed and it is demonstrated how the method can be used to simulate 2D axially symmetric gas flows.

Keywords: SPH-method, axially symmetric flows, the least action principle, Lagrangian fluid dynamics, central difference schemes, a modified predictor-corrector method, the problem of an intense explosion.







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