The interstellar medium (ISM) is inhomogeneous, with clouds of various temperatures and densities embedded in a tenuous intercloud medium. Shocks propagating through the ISM can ablate or destroy the clouds, at the same time significantly altering the properties of the interc10ud medium. This paper presents a comprehensive numerical study of the simplest case of the interaction between a shock wave and a spherical cloud, in which the shock far from the cloud is steady and planar, and in which radiative losses, thermal conduction, magnetic fields, and gravitational forces are aU neglected. As a result, the problem is completely specified by two numbers: the Mach number of the shock, M, and the ratio of the density of the cloud to that of the intercloud medium, X. For strong shocks we show that the dependence on M scales out, so the primary independent parameter is X. Variations from this simple case are also considered: the potential effect of radiative losses is assessed by calculations in which the ratio of specific heats in the cloud is 1.1 instead of 5/3; the effect of the initial shape of the cloud is studied by using a cylindrical cloud instead of a spherical one; and the role of the initial shock is determined by considering the case of a cloud embedded in a wind.Local adaptive mesh refinement techniques with a second-order, two-fluid, two-dimensional Godunov hydrodynamic scheme are used to address these problems, allowing heretofore unobtainable numerical resolution. Convergence studies to be described in a subsequent paper demonstrate that -.. 100 zones per cloud radius are needed for accurate results; previous calculations have generalJy used about a third of this number. The results of the calculations are analyzed in terms of global quantities which provide an overall description of the shocked cloud: the size and shape of the cloud, the mean density, the mean pressure, the mean velocity, the velocity dispersion, and the total circulation.The principal result of the calculations is that small clouds are destroyed in several cloud crushing times, where the doud crushing time tee is the characteristic time for the shock to cross through the cloud. (Quantitatively, tee = Xl/2aO/Vb' where ao is the initial cloud radius and Vb is the velocity of the shock in the intercloud medium.) This result, which is consistent with that of Nittman, Fane, & Gaskell (1982) based on calculations at lower resolution, is contrary to the naive expectation that the destruction of the cloud would occur only after it had swept up a column density of intercloud material comparable to that of the initial cloud, which requires a time of order Xl/ltCC' A model in which the Kelvin-Helmholtz instability fragments the cloud into successively smaller pieces is consistent with the numerical results. Contrary to the conclusion of Nittman et al. (1982), cloud material can be accelerated to high velocity by the passage of the shock; a model for the cloud acceleration is developed. A quantitative model for the generation of vorticity in the...

We present an algorithm for solving the heat equation on irregular time-dependent domains. It is based on the Cartesian grid embedded boundary algorithm of Johansen and Colella (J. Comput. Phys. 147(2):60-85) for discretizing Poisson's equation, combined with a second-order accurate discretization of the time derivative. This leads to a method that is second-order accurate in space and time. For the case where the boundary is moving, we convert the moving-boundary problem to a sequence of fixed-boundary problems, combined with an extrapolation procedure to initialize values that are uncovered as the boundary moves. We find that, in the moving boundary case, the use of Crank-Nicolson time discretization is unstable, requiring us to use the L0-stable implicit Runge-Kutta method of Twizell, Gumel, and Arigu.

We present a finite difference method for solving the equations of combustion in the limit of zero Mach number. In this limit, acoustic waves are weak and do not contribute significantly to the fluid dynamics or energetics. For the equations describing this limit, we construct an efficient. high-resolution numerical method that allows for large temperature and density variations and correctly acCOl.ll1ts for expansion due to heat release.The method, a projection method, is a second order fractional step scheme. In the first step, we compute the solution to advection-reaction-diffusion equations for the velocity, temperature, and species. In the second step, we impose the constraint on the divergence of the velocity field that represents the effect of bulk compression and expansion of the fluid due to heat release. We demonstrate our method on the problem of combustion in an enclosed container.

i o n s w i t h D r . George U l l r i c h and D r . A l l e n Kuhl a r e very much a p p r e c i a t e d . m a n u s c r i p t f o r t h i s r e p o r t a r e acknowledged w i t h thanks.We thank a l s o Ms. Karen H i b b e r t f o r h e r h e l p i n t h e l a t t e r t a s k .The e f f o r t s of Ms. Mary S t r o i k on t h e many v e r s i o n s o f t h e The f i n a n c i a l a s s i s t a n c e r e c e i v e d f r o m t h e U.S. Department o f Energy a t t h e Lawrence B e r k e l e y L a b o r a t o r y under C o n t r a c t DE-AC03-78SF00098; f r o m t h e U.S.Defense N u c l e a r Agency under DNA Task Code Y99QAXSG and DNA C o n t r a c t 00183-C-0266; f r o m t h e Naval S u r f a c e Weapons C e n t e r Independent Research Fund; ii Summary An e x t e n s i v e s e r i e s o f ntrmerical c a l c u l a t i o n s of oblique-shock-wave r e f l e c t i o n s i n a i r and argon have been performed u s i n g a v e r s i o n o f t h e second-order E u l e r i a n Godunov scheme f o r i n v i s c i d c o m p r e s s i b l e f l o w . T h i s scheme i s among t h e b e s t o f t h e upwind schemes developed i n r e c e n t y e a r s .The r e s u l t s have been compared w i t h t h e b e s t a v a i l a b l e i n t e r f e r o m e t r i c data from t h e lITIAS 10 cm x 18 cm shock tube, f o r f i f t e e n d i f f e r e n t cases. A s i g n i f i c a n t p o r t i o n of o u r a n a l y s i s i s devoted t o t h e q u e s t i o n o f t h e F u r t h e r p a r a n e t r i z e d s e r i e s o f c a l c u l a t i o n s were performed i n an e f f o r t t o study t h e f e a s i b i l i t y of n u m e r i c a l l y c o n s t r u c t i n g i n v i s c i d t r a n s i t i o n l i n e s i n t h e (MS, e )-plane. Good agreement w i t h a n a l y t i c p r e d i c t i o n s was f o u n d f o r low values of p.1, and, as m i g h t be expected, t h e r e a r e s u b s t a n t i a l d i s c r e p a n c i e s f o r M, = 8.75. i n t h e f o r m u l a t i o n o f a c c u r a t e t r a n s i t i o n c r i t e r i a i s discussed. O v e r a l l , t h e computer code has been found t o r e p r e s e n t a s i g n i f i c a n t p r e d i c t i v e c a p a b i l i t y . d e t a i l e d m o d e l l i n g o f n o n e q u i l i b r i u m and viscous e f f e c t s i s , however, an i m p o r t a n t o b j e c t i v e . The o b j e c t i v e o f t h i s p o r t i o n o f t h e s t u d y was t o assess t h e accuracy o f t h eThe f u t u r e e x t e n s i o n o f t h e code t o p e r m i t t h e iii

Recent experimental and numerical studies of weak Mach reflections are examined. It is shown that the fundamental reason for the von Neumann paradox is that his theory of Mach reflection is based on the assumption that the flow downstream of the reflected wave and the Mach shock near the wave triple point is uniform. The assumption is shown to be valid for strong Mach reflection which agrees with experiment, but invalid for weak Mach reflection whicb does not agree with experiment. It is also shown that viscous effects are dominant when the incident shock is within about 100 mean free path lengths of the corner, but not otherwise. The analytical theory of the entire subsonic region supports these conclusions.* Results based on conclusions made at the" Workshop on weak Mach reflection", March 31 ~April 1, '88 at Tokyo Denki University.