AN APPROXIMATE DESCRIPTION OF DISCONTINUITY BREAKUP IN FLOW CALCULATIONS WITH THE GODUNOV SCHEME

U. N. Derugin, I. P. Кasакоva, M. M. Prоshin, B. P. Tikhomirov
VANT. Ser. Mat. Mod. Fiz. Proc 1991. Вып.2. С. 79-81.

      A widely used discontinuity breakup model is considered based on replacing rarefaction waves by rarefaction "jumps" assuming that left and right quantities differ only slightly. Numerical results of shock-initiated nozzle and detonation ware propagation from a closed tube and calculations with the Godunov scheme are analyzed. For this type of problems, an approximate discontinuity breakup model is shown to give errors in the numerical solution and to distort the results. The calculations indicate that more accurate models must be used in the Godunov scheme.

      A method is proposed for developing conservative difference schemes with arbitrary hexahedron cells for three-dimensional heat conduction equation. For a difference scheme to be constructed, auxiliary temperatures are introduced on edges and surfaces in addition to wasic quantities, that is cell-centered temperatures. Temperatures in the middle point of the edges are determined by linear interpolation in terms of coordinate line curvatures. A cell-centered temperature is derived from flux and temperature continuity conditions. For unidirectional flux calculations, the scalar function gradient is splitted into three linearly independent vectors with vector directions chosen so that coefficients are nonnegative in a difference expression for the flux. This condition provides the equation resolution for defining a surface-centered temperature.