A pseudospectral method for solution of the three-dimensional incompressible Navier-Stokes equations

Ku, Hwar-Ching; Hirsh, R. S.; Taylor, Thomas D.

doi:10.1007/bfb0041822

Cited by 61 publications

(109 citation statements)

References 7 publications

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“…To study the impact of hybrid interpolation in predicting three dimensional flows, we now evaluate it using a threedimensional flow in a cubic lid-driven cavity (Fig. 14) with the reference data from Ku et al (1987). The size of the cavity is 1 m × 1 m × 1 m and the Reynolds number is 1000.…”

Section: Three-dimensional Flow In Cubic Liddriven Cavitymentioning

confidence: 99%

Reduction of Numerical Diffusion in FFD Model

Jin

Chen

2012

Engineering Applications of Computational Fluid Mechanics

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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.

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Section: Three-dimensional Flow In Cubic Liddriven Cavitymentioning

confidence: 99%

Reduction of Numerical Diffusion in FFD Model

Jin

Chen

2012

Engineering Applications of Computational Fluid Mechanics

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“…9, 10 and 11 we compare the u-velocity distribution along the vertical centerline (x=0.5) and the v-velocity distribution along the horizontal centerline (y=0.5), at the cavity symmetry plane (z=0.5). The comparison is made with the numerical results of the pseudospectral method of Ku et al (1987) who used 25x25x13 modes for Re=100,400 and 31x31x16 modes for Re=1000. Our results agree well with those of Ku et al (1987).…”

Section: Results and Validationmentioning

confidence: 99%

“…The comparison is made with the numerical results of the pseudospectral method of Ku et al (1987) who used 25x25x13 modes for Re=100,400 and 31x31x16 modes for Re=1000. Our results agree well with those of Ku et al (1987). The positions and values of velocity extrema are in good agreement.…”

Section: Results and Validationmentioning

confidence: 99%

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Artificial Compressibility 3-D Navier-Stokes Solver for Unsteady Incompressible Flows with Hybrid Grids

Vrahliotis

Pappou

Tsangaris

2012

Engineering Applications of Computational Fluid Mechanics

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An unsteady incompressible numerical method for the solution of Navier-Stokes equations is presented. The finite volume solver adopts the method of artificial compressibility, using an implicit dual time stepping scheme for time accuracy. The 2D solver operates on general hybrid meshes containing triangles and quadrilaterals, while the 3D solver operates on hybrid meshes containing tetrahedra, pyramids, prisms and hexahedra. The developed algorithms for spatial discretization and time integration are mesh transparent. An upwind spatial discretization scheme is used for the convective terms and a central scheme for the diffusive terms. Efficient calculation of flow fluxes is implemented in an edge-wise fashion. A new combined method for efficient and accurate evaluation of variable gradients is achieved by using an averaging technique and by avoiding multiple spatial integration of the same element of the mesh. The results obtained agree well with numerical solutions obtained by other researchers.

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“…The popularity of this benchmark comes from its ability to generate rich flow structure while maintaining a simplified geometrical shape and boundary condition. Flow field in the lid-driven cavity has been studied extensively both experimentally (Aidun et al, 1991) and numerically (Albensoeder and Kuhlmann, 2005;Ku et al, 1987).…”

Section: Driven Cavity Benchmarkmentioning

confidence: 99%

Real-time flow simulation of indoor environments using lattice Boltzmann method

et al. 2015

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A novel lattice Boltzmann method (LBM) -based 3D computational fluid dynamics (CFD) technique has been implemented on the graphics processing unit (GPU) for the purpose of simulating the indoor environment in real-time . We study the time evolution of the turbulent air flow and temperature inside a test chamber and in a simple model of a four-bed hospital room. The predicted results from LBM are compared with traditional CFD-based large eddy simulations (LES). Reasonable agreement between LBM results and LES method are observed with significantly faster computational times.

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A pseudospectral method for solution of the three-dimensional incompressible Navier-Stokes equations

Cited by 61 publications

References 7 publications

Reduction of Numerical Diffusion in FFD Model

Reduction of Numerical Diffusion in FFD Model

Artificial Compressibility 3-D Navier-Stokes Solver for Unsteady Incompressible Flows with Hybrid Grids

Real-time flow simulation of indoor environments using lattice Boltzmann method

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