M. Behr, Rice MEMS - Flows in Complex Geometries

Simulation of Incompressible Flows Around 3D Complex Objects

[CFD Picture]

Figure 1: Surface mesh for the submarine.

[CFD Picture]

Figure 2: Pressure distribution on the submarine.

A basic building block of the CFD research outlined here is the ability to model steady and time-dependent fluid flows around complex three-dimensional objects. To accomplish this task, a fluid flow solver based on finite element methodology has been developed. It is based on the velocity-pressure formulation of the Navier-Stokes equations. The variational form of these equations is stabilized using Least Squares (LS) or, alternatively, Streamline-Upwind/Petrov-Galerkin (SUPG) techniques in order to provide robust and accurate solutions at high Reynolds numbers. Consistent stabilization via LS terms or additional Pressure-Stabilizing/Petrov-Galerkin (PSPG) terms also allows the use of equal-order interpolation functions for the velocity and pressure variables. The equations are discretized in time using either a standard semi-discrete central-differencing approach or a higher-order accurate space-time technique. Simple turbulence models, such as the Smagorinsky model, are used for computations involving high Reynolds numbers. The scalable flow solver is implemented in Fortran and C and has been used on a range of parallel architectures, including Cray T3D/E, IBM SP2 and Intel Paragon. The interprocessor communication is accomplished using a range of communication libraries, including MPI, PVM and SHMEM, of which any single one may be selected to suit a particular computing platform. An older, data parallel version of this solver, is also in use on the Connection Machine CM-5. As an example application, this flow solver has been used to compute water flow around a Los Angeles-class submarine at Reynolds number 1x10⁹. Figure 1 shows the surface of the unstructured volume mesh, which consists of 504,000 tetrahedral elements. Figure 2 shows the steady pressure contours on the submarine hull.