Truncation error terms in the kinetic energy calculation in the HELP algorithm and their consequences

Abstract

When the HELP computer code is applied to conical-shaped charge warhead problems, the computed internal energy predicts a thermal state completely different than that indicated by experiments. The cause of this phenomenon is the numerical interchange of the kinetic energy to internal energy which is generated by terms of the order of the truncation error in the kinetic energy calculation. A correction is given and qualitative thermal agreement is achieved for the first time between a HELP calculation and experimental evidence. The effects of the original kinetic energy calculation on the accuracy of the internal energy is problem dependent and criteria for such a determination are given in terms of the truncation error terms for the internal energy. A mesh refinement study further illustrates the consequences of the original and modified kinetic energy calculations. The same phenomenon can occur in other computer codes with a Particle-In-Cell based algorithm and the given correction is applicable.