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An immersed boundary method for complex terrain flow analysis

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Abstract

We present modified immersed boundary method (IBM) for complex terrain flow analysis which is done on coarse grid and based on large-eddy simulation (LES). The main idea is that IBM force to make fluid velocity perpendicular to terrain surface zero and to revive tangential fluid velocity near the terrain surface is applied at Lagrangian point on terrain surface. For smoothing out the effect of IBM force on coarse grid, IBM force at Lagrangian point is distributed on collocated grid and gathered at the position of fluid velocity on staggered grid. For validation of our method, we conduct complex terrain flow analysis for mountainous terrain which is mock-up model of coastal region in Gyeongju and compare our simulation results with wind-tunnel experiment results and other simulation using ANSYS. Our simulation results show better agreement with wind-tunnel experiment results than ANSYS simulation results and properly capture various flow characteristics occuring in complex terrain.

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Abbreviations

u i :

Fluid velocity for i direction

p :

Pressure

τ ij :

Subgrid-scale stress tensor

ρ :

Density of air

ν :

Kinematic viscosity of air

ν T :

Eddy viscosity

C v :

Vreman model coefficient

C s :

Smagorinsky model coefficient

x :

Position of Eulerian grid point

X l :

Position of Lagrangian point

X j :

Position of intersection point

ΔA :

Surface area of a Lagrangian point

ΔV :

Volume of a Lagrangian point

Δv :

Volume of an Eulerian cell

u s i :

Fluid velocity on staggered grid for i direction

u c i :

Fluid velocity on collocated grid for i direction

U i :

Fluid velocity at Lagrangian point in tensor notation

F i :

Force on Lagrangian point in tensor notation

U l :

Fluid velocity at Lagrangian point in vector form

F l :

Force on Lagrangian point in vector form

U l n :

Normal component of Ul to terrain surface

U lt :

Tangential component of Ul to terrain surface

C :

The constant for near-slip condition

f s i :

Force due to IBM on staggered grid for i direction

f c i :

Force due to IBM on collocated grid for i direction

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Acknowledgments

We are grateful to the Agency for Defense Development of Korea for the support (UD180049GD).

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Authors and Affiliations

  1. School of Mathematics and Computing, Yonsei University, Seoul, 03722, Korea

    Jaewook Nam & Changhoon Lee

  2. Department of Mechanical Engineering, Yonsei University, Seoul, 03722, Korea

    Changhoon Lee

Authors
  1. Jaewook Nam
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  2. Changhoon Lee
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Corresponding author

Correspondence to Changhoon Lee.

Additional information

Jaewook Nam received his B.S. (2018) from Yonsei University, Seoul, Korea., in Mechanical Engineering. He is an integrated Ph.D. student in the School of Mathematics and Computing, Yonsei University, Korea. His research interests include Large-eddy simulation, immersed boundary methods, and the area of incompressible fluid dynamics.

Changhoon Lee received his B.S. (1985) and M.S. (1987) from Seoul National University, Seoul, Korea and Ph.D. (1993) from UC Berkeley, USA., in Mechanical Engineering. He is a Professor in the School of Mathematics and Computing and Department of Mechanical Engineering, Yonsei University, Korea. His research interests include fundamentals of turbulence, particle-turbulence interaction, numerical algorithms, air pollution modeling and stochastic process.

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Nam, J., Lee, C. An immersed boundary method for complex terrain flow analysis. J Mech Sci Technol 36, 1817–1824 (2022). https://doi.org/10.1007/s12206-022-0318-0

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  • DOI: https://doi.org/10.1007/s12206-022-0318-0

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