EMPLOYMENT OF GODUNOV METHOD ON UNSTRUCTURED GRIDS TO SOLVE CONTINUUM MECHANICS PROBLEMS

I.N. Lomov, V.I. Kondaurov
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.1. С. 58.

      The Godunov method and higher order methods constructed on its base are widely used in aerodynamics to solve hyperbolic systems of the laws of conservation. The results found show that the method provides considerable opportunities for solving these problems. Therefore, it is interesting to use these methods to solve condensed media mechanics problems as it is necessary to take into consideration both smooth and discontinuous solutions. The Godunov type methods should be based on a closed divergence form equation system. The divergence equations of continuity, conservation of momentum and energy are well known, but the equation for the symmetric strain tensor can not basically be written in the divergent form and is replaced with the law of conservation of the velocity and strain consistency which uses the asymmetric distortion (strain gradient) tensor [1]. The laws of conservation are closed with the governing relations: the wide-range equation of state and kinetic equations of damageability increase and plastic strains. This approach corresponds to the elastic-viscous-plastic model and removes the problems relating to the impossibility of the full divergent form for the scleronomous elastic-plastic model.
      For that equation system the Riemann problem was solved with method [2] using the parabolic approximation. When solving the Riemann problem between boundary and imaginary cells various boundary condition types may be set. The method is implemented on an arbitrary movable Lagrangian-Eulerian grid. To determine the cells used in the finite-volume formulation of the laws of conservation, the Delaunay triangulation of the computational domain is used.
      The program system developed was used to compute various problems, for example, of high- speed collision, space body motion in the planet atmosphere, high-energy effects, on condensed targets. These computations showed the capability of the method to model shock waves, phase transitions, inelastic finite strains and condensed medium damageability accumulation.
      1. Kondaurov V.I., Nikitin L.V. Theoretic fundamentals of geomaterial reology. ?.: Nauka Publishers, 1990.
      2. Dukowicz J. //J. Comput. Phys. 1985. Vol. 61. P. 119.