**Monday, October 23/11:00 AM**

## IP2

An Adaptive Projection Method
for Low Mach Number Flows

A number of fluid dynamics problems of engineering and environmental importance are described by models in which the flow velocity is small in terms of Mach number but for which compressibility plays an important role. Accurate modeling of NOx formation in an industrial burner must treat expansions due to heat release; accurate modeling of transport of pollutants in the atmosphere must account for changes in atmospheric pressure as a function of altitude. In the first part of this talk, the speaker will discuss some approaches to designing numerical methods for these types of low-Mach number, advectively-dominated time-dependent fluid flows. The approach is based on two ideas: (1) the use of low-Mach number asymptotics to eliminate acoustic waves, and of the Hodge/Helmholtz projection to express the resulting elliptic constraint equations; and (2) the use of a predictor-corrector time discretization to split of the equations into hyperbolic and second-order elliptic/parabolic terms, with appropriate strategies for discretizing each. In the second part of the talk, he will discuss how these numerical methods can be incorporated into a local adaptive mesh refinement algorithm. He will present some examples of the application of this methodology to several types of low Mach number flows.
**John B. Bell**

Center for Computational Sciences and Engineering

Lawrence Livermore National Laboratory

7/21/95