## Fsheetx Msg Cfd Phi3d

POC: David M. Hetrick (865)576-7556/hetrickdm@ornl.gov http://computing.ornl.gov/cse_home/cms/cmshome.shtml Scientific Computing within the ORNL Modeling & Simulation Group: CFD Code Development - PHI3D The ORNL Modeling and Simulation Group (MSG) develops sophisticated numerical solutions for a wide range of scientific, engineering, and operational applications. MSG's core competency is computational physics and engineering, and within our computational fluid dynamics (CFD) focus area we have developed the general purpose computational fluid dynamics (CFD) code PHI3D. As the CFD field continues to mature, algorithms are required to exploit the most recent advances in approximation theory, numerical mathematics, computing architectures, and hardware. Meeting this requirement is particularly challenging in incompressible fluid mechanics, where primitive-variable CFD formulations that are robust, while also accurate and efficient in three dimensions, remain an elusive goal. MSG is engaged in algorithmic research with the aim of developing an in-house CFD code for three-dimensional incompressible fluid flows. The result of this research is the new Continuity Constraint Method (CCM) as implemented in the PHI3D code.

The theoretical basis for the CCM consists of a finite-element spatial semi-discretization of a Galerkin weak statement, equal-order interpolation for all state-variables, a 0-implicit time-integration scheme, and a quasi-Newton iterative procedure extended by a Taylor Weak Statement formulation for dispersion error control. In contrast to the general family of pressure-relaxation incompressible CFD algorithms, the CCM does not use the pressure as merely a mathematical device to constrain the velocity distribution to conserve mass. Rather, the mathematically-smooth, physically- motivated genuine pressure is an underlying replacement for the non-smooth, continuity-constraint function to control inherent dispersive error mechanisms. The genuine pressure is calculated by the diagnostic pressure Poisson equation, evaluated using the verified solenoidal velocity field. The results of a PHI3D window-cavity test case are depicted in the accompanying figure which shows typical 3D window-cavity flow behavior. PHI3D is an extremely versatile CFD resource for a broad range of R&D, industrial, homeland defense, and military applications. We welcome the opportunity to discuss your potential applications and ways PHI3D can contribute to a solution.

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Results from validation & verification effort for the MSG-developed PHI3D code. Graphic shows incompressible, laminar, buoyancy-driven flow between separate hot & cold rooms. Release point is bottom of the door between the rooms, & tracks are color- coded by temperature.