Stability analysis of the von Neumann-Richtmyer difference scheme with rate dependent materials relations. Part 2: Subcycling and the Malvern relation

Stability criteria are developed for solving problems involving rate-dependent material properties in hydrocodes such as WONDY. As severe restrictions in the allowable timestep size result for small relaxation times, subcycling was introduced to solve this problem. That is, if the subcycle number (m) is large enough, then the timestep restriction as it exists in WONDY is sufficient for stability; this is shown herein for the case of a simple backward difference subcycling scheme for the Malvern rate-dependent material relation. The problem of precisely how large m must be for a given ratio of the timestep to the relaxation time, h = Delta t/tau, was studied. Although the form of solution for m as a function of h is complicated, it can be incorporated easily into WONDY. In the extreme cases of h very small or large, the solution can be simply stated: if h is very small, then m = 1 suffices; if h is greater than 2, then m greater than or equal to h suffices.