METHOD AND CODE FOR THE EVALUATION OF THE TOTAL INTERSECTION VOLUME OF TWO ARBITRARILY LOCATED IN SPACE HEXAHEDRA WITH NONPLANE FACES

V.I. Delov, L.V. Dmitrieva, V.V. Sadchikov
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.1. С. 47.

      The report is devoted to the description of the method developed for the calculation of spatial problem of the intersection of two arbitrarily located in space; hexahedra and evaluation of their total volume of intersection, if any. The need in such algorithms and codes occurs particularly in the calculation of gas-dynamic problems in Lagrangian coordinates. It is known that in this case the numerical calculation of complicated problems necessitates one-shot grid reconfiguration and rescaling the values to the new grid because further computations are impossible. These situations are encountered, for example, in the event of strong grid distortions, pinch of physical domains, formation of small-scale jet flows.
      The calculation of the problems presented here is also addressed when creating Lagrangian-Eulerian methods for continuum mechanics problems with strong deformations. In addition, such algorithms are extremely needed to create the graphics packages and codes, oriented to the operation with 3-D geometrical objects.
      The problem solution reduces to finding the exact intersection volume of two tetrahedra arbitrarily located in space.
      The methods are considered to split the polyhedra into elementary tetrahedra together with the main program implementation features for the algorithms proposed. The most computationally cost efficient ways are reported to divide the polyhedra without additional computational errors.
      The report presented the results of test computations for the intersection of hexahedra with the faces representing second order surfaces-hyperbolic paraboloids that are used in 3-D “D” code.

      The report presented the results of numerical simulation of X-ray recording detonation initiation and evolution in a plane HE layer from a linear initiator located on the surface of a plane layer confined with a steel plate from the opposite side. When the diverging wave is reflected from a steel barrier a shock or detonation wave is generated (depending on HE layer thickness) which propagates along the barrier surface. With decreasing HE thickness a delay in detonation propagation along the layer is observed. This effect is a significant characteristic of shock-wave HE sensitivity and accuracy of its simulation which was made by 2-D gas-dynamical programs using the detonation kinetics model. The computed result reproduces the experimental picture fairly well.