Reduction of Numerical Diffusion in FFD Model

Abstract Fast flow simulations are needed for some applications in building industry, such as the conceptual design of indoor environment or teaching of Heating Ventilation and Air Conditioning (HVAC) system design in classroom. Instead of pursuing high accuracy, those applications require only conceptual distributions of the flow but within a short computing time. To meet these special needs, a Fast Fluid Dynamics (FFD) method was proposed to provide fast airflow simulation with some compromise in accuracy. This study is to further improve the FFD method by reducing the numerical viscosity that is caused by a linear interpolation in its semi-Lagrangian solver. We propose a hybrid scheme of a linear and a third-order interpolation to reduce the numerical diffusion in low order scheme and the numerical dispersion in high order scheme. The FFD model with both linear and hybrid interpolations are evaluated by simulating four different indoor flows. The results show that the hybrid interpolation can significantly improve the accuracy of the FFD model with a small amount of extra computing time.

[1]  G. D. Davis.  Natural convection of air in a square cavity: A bench mark numerical solution , 1983 .

[2]  Vivek Sarin,et al.  Numerical Simulation of Mixed Convective Flow Over a Three-Dimensional Horizontal Backward Facing Step , 2005 .

[3]  W. Zuo,et al.  Impact of Time-splitting Schemes on the Accuracy of FFD Simulations , 2011 .

[5]  Wangda Zuo,et al.  Fast and informative flow simulations in a building by using fast fluid dynamics model on graphics processing unit , 2010 .

[6]  U. Ghia,et al.  High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method , 1982 .

[7]  Jonathan M. Cohen,et al.  Low viscosity flow simulations for animation , 2008, SCA '08.

[8]  André Robert,et al.  A stable numerical integration scheme for the primitive meteorological equations , 1981 .

[9]  P. Moin,et al.  Application of a Fractional-Step Method to Incompressible Navier-Stokes Equations , 1984 .

[10]  Jos Stam,et al.  Stable fluids , 1999, SIGGRAPH.

[11]  Ronald Fedkiw,et al.  Visual simulation of smoke , 2001, SIGGRAPH.

[12]  M. Das,et al.  A FINE GRID SOLUTION FOR A LID-DRIVEN CAVITY FLOW USING MULTIGRID METHOD , 2009 .

[13]  Qingyan Chen,et al.  Ventilation performance prediction for buildings: A method overview and recent applications , 2009 .

[14]  Qingyan Chen,et al.  Improvements in FFD Modeling by Using Different Numerical Schemes , 2010 .

[15]  Manab Kumar Das,et al.  Conjugate Mixed Convection Heat Transfer in Plane Laminar Wall Jet Flow , 2009 .

[16]  Q Chen,et al.  Real-time or faster-than-real-time simulation of airflow in buildings. , 2009, Indoor air.

[17]  G. de Vahl Davis,et al.  Natural convection in a square cavity: A comparison exercise , 1983 .

[18]  James W. Axley,et al.  Multizone Airflow Modeling in Buildings: History and Theory , 2007 .

[19]  B. Armaly,et al.  Experimental and theoretical investigation of backward-facing step flow , 1983, Journal of Fluid Mechanics.

[20]  I. E. Barton,et al.  Laminar flow past an enclosed and open backward‐facing step , 1994 .

[21]  R. Courant,et al.  Über die partiellen Differenzengleichungen der mathematischen Physik , 1928 .

[22]  Adrian Bejan,et al.  The “Heatline” Visualization of Convective Heat Transfer , 1983 .

[23]  Anupam Dewan,et al.  A Multigrid-Accelerated Code on Graded Cartesian Meshes for 2D Time-Dependent Incompressible Viscous Flows , 2010 .

[24]  Charles L. Merkle,et al.  Solution-limited time stepping to enhance reliability in CFD applications , 2009, J. Comput. Phys..

[25]  Hyeong-Seok Ko,et al.  Stable but nondissipative water , 2005, TOGS.

[26]  B. P. Leonard,et al.  A stable and accurate convective modelling procedure based on quadratic upstream interpolation , 1990 .

[27]  H. L. Seegmiller,et al.  Features of a reattaching turbulent shear layer in divergent channel flow , 1985 .

[28]  Jie Liu,et al.  Open and traction boundary conditions for the incompressible Navier-Stokes equations , 2009, J. Comput. Phys..

[29]  T. Taylor,et al.  A Pseudospectral method for solution of the three-dimensional incompressible Navier-Stokes equations , 1987 .

[30]  A. Chorin.  A Numerical Method for Solving Incompressible Viscous Flow Problems , 1997 .

[31]  F. Durst,et al.  Experimental studies of high Reynolds number backward-facing step flow , 1985 .

[32]  Standard Ashrae.  Thermal Environmental Conditions for Human Occupancy , 1992 .

[33]  M. Kopera.  Direct numerical simulation of turbulent flow over a backward-facing step , 2011 .