Research Objectives
Many phenomena in fluid dynamics are described by low Mach number models. Examples of low Mach number flows range from propagation of flames and the breakup of sprays to the dynamics of the atmosphere and the oceans. The goal of this project is to develop new computational tools for modeling these types of flows.
Computational Approach
Our approach for modeling low Mach number flows is based on a projection formulation that incorporates modern high-resolution upwind difference methodology for discretizing advective transport. This formulation forms the basis for a hierarchical adaptive-mesh refinement algorithm that localizes computational effort where it is required to preserve accuracy.
Accomplishments
We completed a serial version of the adaptive-mesh refinement algorithm for the incompressible Navier-Stokes equations, which is a prototype for more general low Mach number flows in both two and three dimensions. This basic framework has also been extended to model laminar flame propagation. We are currently developing a parallel version of the algorithm for the T3E, based on a coarse-grained parallelization strategy.
Significance
Successful completion of this work will provide us with a dramatic improvement in our ability to model low Mach number flows. This improvement in modeling capability will enable us to gain new insights into fundamental scientific questions about turbulent flows and combustion and will form the basis of a new generation of modeling tools that can be used for designing combustion systems such as engines and industrial furnaces.
Publications
Almgren, A. S., J. B. Bell, P. Colella, L. H. Howell, M. L. Welcome. N.d. A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations. J. Comput. Phys., in press.
Pember, R. B., P. Colella, L.H. Howell, A. S. Almgren, J. B. Bell, W. Y. Crutchfield, V. E. Beckner, K. C. Kaufman, W. A. Fiveland, J. P. Jessee. 1997. An adaptive projection method for the modeling of unsteady, low Mach number combustion. Fall Meeting of the Western States Section of the Combustion Institute. WSS/CI 97F-125. LBL-38551.
Howell, L. H., R. B. Pember, P. Colella, J. P. Jessee, and W. A. Fiveland. N.d. A conservative adaptive-mesh algorithm for unsteady, combined-mode heat transfer using the discrete ordinates method. Numerical Heat Transfer, Part B: Fundamentals, submitted.
URL
Vorticity magnitude from the 3D simulation of a variable density shear layer using adaptive
mesh refinement.