In Sussman, Smereka and Osher (1994), a numerical method using the level set approach was formulated for solving incompressible two-phase flow with surface tension. In the level set approach, the interface is represented as the zero level set of a smooth function; this has the effect of replacing the advection of density, which has steep gradients at the interface, with the advection of the level set function, which is smooth. In addition, the interface can merge or break up with no special treatment. We maintain the level set function as the signed distance from the interface in order to robustly compute flows with high density ratios and stiff surface tension effects. In this work, we couple the level set scheme to an adaptive projection method for the incompressible Navier-Stokes equations, in order to achieve higher resolution of the interface with a minimum of additional expense. We present two-dimensional axisymmetric and fully three-dimensional results of air bubble and water drop computations.

No abstract

DISCI.AIMER Thi~ document luas prepared .~ an account of work sponsored b)' an .Keft('~' of the Uniled Slates Go'ternment. Neither the United States Gonrnment ~r the Uni\'ersit), of C.morai. nor an)' of their employees., m.akes aay "arnnly. npress or implied. or assumes .n~' le.allillbilit) or responsibility for the attUrae). completeness.. or asefulness of an) inform.alion. apparatus. produd. or p~ diSC'losed. or reprewnts that its usc "'ol.lld not infringe privattl}' O'I"ned rights. Re(ereMe herein ' 0 an)' specific commerdal products. process. or service b) trade name. trademark. manuladurer. or other"'ise. does not necessaril), can.titute or imply Us t'ndorseme-nt. recommendation. or fa\lorina b~' the United States Government or tbe Universit)' of California. The "jews and opinions or authors npressed herein do not neces.saril,' stale or renect those of the United States Governmenl or the Universit) of California. and shaU not be used for ad\ertisina or prodoct endorsement purposes.. .

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.

No abstract