### Thrust Leader: Dr. Clarence Burg, Mathematics

Computational Fluid Dynamics (CFD) is the study of fluid motion via computational simulations. Applications include air flow past wings and cars, around propellers and through turbines, water flow through rivers, man-made aqueducts and underground aquifers, and air flow involved in weather phenomena. CFD involves numerical mathematics, an understanding of various physical laws and phenomena and high performance computing.

Physically, the fluid phenomena is modeled via physical laws, such as the conservation of mass, momentum and energy, and various molecular models to determine turbulence and the effects of random processes within the fluid. These models result in complicated mathematical expressions, typically involving partial derivatives of space and time. As the physical phenomenon is modeled more accurately, these mathematical equations become more complicated, so that exact algebraic solutions rarely exist. Thus, the solution to the mathematical equations are numerically approximated, via various approaches involving high performance computing.

The process of performing a CFD simulation involves the following steps:

1. Selection of the appropriate mathematical model for the physical phenomenon - 2D versus 3D, compressible (air) versus incompressible (water), inviscid (no friction) versus viscous (with friction).

2. Creation of the geometry - the shape of the river, the wing, the car or the submarine, the elevation of the ground, etc.

3. Discretization of the computational domain into a finite set of discrete locations, called a computational mesh or computational grid.

4. Approximation of the solution of the mathematical model at the discrete locations within the computational domain - the pressure, density, temperature and velocity at each location within the fluid flow.

5. Visualization of the pressure distribution, the velocity field, particle traces and isosurfaces.

6. Analysis of the numerical results to determine whether the approximation is sufficiently accurate for the physical phenomenon and to learn about the behavior of the physical phenomenon.

7. Refinement of the mathematical model, the geometry, the computational grid and the numerical approximation to obtain a more accurate numerical approximation.

Researchers within the CFD Thrust will have access to the following software:

1. **SolidMesh** (SimCenter, Mississippi State University) - software for creation and manipulation of geometries.

2. ** AFLR2** / **ALFR3** (David Marcum, Mississippi State University) - unstructured grid generation software in 2D and 3D.

3. **U ^{2}NCLE** (SimCenter, Mississippi State University) - unstructured CFD software for compressible (air) and incompressible (water) simulations, appropriate for flow past airplane wings, helicopter propellers, turbines and submarines.

4. **FUN3D **(NASA Langley) - unstructured CFD software for compressible simulations of air past airplanes, rockets and re-entry vehicles.

5. **Camel** (Jackson State University) - unstructured CFD software for compressible and incompressible simulations, appropriate for airplanes and surface ships.

6. **WRF** - Weather Research Forecasting (National Center for Atmospheric Research) - structured meteorological simulation, at the regional, national and global levels.

7. ** VisIt** (Lawrence Livermore National Lab) - visualization software.

Current research projects:

1. Supersonic wing without sonic boom.

2. Comparison of numerical results from various CFD software packages

3. Helmholtz resonator simulations

4. High resolution weather modeling to study influence of surface terrain on local weather phenomena.