VERIFICATION TEST PROBLEMS
We present analytic solutions to two test problems that can be used to check the hydrodynamic implementation in computer codes designed to calculate the propagation of shocks in spherically convergent geometry. Our analysis is restricted to fluid materials with constant bulk modulus. In the first problem we present the exact initial acceleration and pressure gradient at the outer surface of a sphere subjected to an exponentially decaying pressure of the form P(t) = P{sub 0}e{sup -at}. We show that finely-zoned hydro-code simulations are in good agreement with our analytic solution. In the second problem we discuss the implosions of incompressible spherical fluid shells and we present the radial pressure profile across the shell thickness. We also discuss a semi-analytic solution to the time-evolution of a nearly spherical shell with arbitrary but small initial 3-dimensional (3-D) perturbations on its inner and outer surfaces.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 923614
- Report Number(s):
- UCRL-PROC-233567; TRN: US200804%%1354
- Resource Relation:
- Conference: Presented at: 15th APS topical conference on Shock Compression of Condensed Matter, Kohala Coast, HI, United States, Jun 24 - Jun 29, 2007
- Country of Publication:
- United States
- Language:
- English
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