Numerical Methods and Modeling

Immersed Boundary Method for Complex Flows

복잡한 형상 물체 주위에 형성되는 유체현상을 고정격자계를 사용하여 해석할 수 있는 가상경계기법 (Immersed Boundary Method)를 개발하였으며, 그 일례로 보행시 발생되는 난류현상을 예측하였다.

An immersed boundary method for time-dependent, three-dimensional, incompressible flows is presented in this paper. The incompressible Navier-Stokes equations are discretized using a low-diffusion flux splitting method for the inviscid fluxes and second-order central-differences for the viscous components. Higher-order accuracy achieved by using weighted essentially non-oscillatory (WENO) or total variation diminishing (TVD) schemes. An implicit method based on artificial compressibility and dual-time stepping is used for time advancement. The immersed boundary surfaces are defined as clouds of points, which may be structured or unstructured. Immersed-boundary objects are rendered as level sets in the computational domain, and concepts from computational geometry are used to classify points as being outside, near, or inside the immersed boundary. The velocity field near an immersed surface is determined from separate interpolations of the components tangent and normal to the surface. The tangential velocity near the surface is constructed as a power-law function of the local wall normal distance. Appropriate choices of the power law enable the method to approximate the energizing effects of a turbulent boundary layer for higher Reynolds number flows. Four different flow problems (flow past a circular cylinder, a NACA0012 airfoil, a sphere, and a stationary mannequin) are simulated using the present immersed boundary method, and the predictions show good agreement with previous computational and experimental results. Finally, the flow induced by realistic human walking motion is simulated as an example of a problem involving multiple moving immersed objects.

Choi et al. (2007) Journal of Computational Physics

Schematic illustrating classification of cell-centered points for a complex immersed body

Evolution of iso-surfaces of streamwise velocity and coherent vertical structures induced human walking motion at each time instant

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Particle Deposition in Human Lungs

인체내 입자점착에 대한 수학모형을 개발하고, 객체, 입자, 환경특성을 고려한 흡수선량 (dosimetry)을 예측하여 대기오염에 따른 인체유해성 평가를 하고자 한다.

A dynamic single-path mathematical model was developed that is capable of analyzing detailed deposition patterns of inhaled particles in human lungs. Weibel’s symmetric lung morphology was adopted as the basic lung structure, and detailed transport processes were evaluated numerically using the fully implicit procedure. Deposition efficiencies by specific mechanisms were individually examined for accuracy and new empirical formulas were incorporated whenever appropriate. Deposition in the alveolar region was divided into deposition fractions in the alveolar duct and alveoli considering active transport processes between the two regions. The deposition fractions were obtained for each airway generation, serial lung volumetric compartments, and conventional three-compartment anatomic lung regions. In addition, the surface dose and cumulative deposition with time were analyzed. The results showed excellent agreement with available experimental data. The present model provides an improvement from the previously reported models and can be used as a tool in assessing internal dose of inhaled particles under various inhalation conditions.

Choi & Kim (2007) Inhalation Toxicology

Schematic diagram of one-dimensional trumpet morphology of human lungs.

Schematic diagram of particle transport and deposition processes in the alveolar region: (a) inspiration and (b) expiration.

Total deposition fraction vs. particle diameter in the normal lung at FRC = 3000 ml for three different breathing patterns.

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Hybrid LES/RANS Methods for Compressible Turbulent Boundary Layer

난류경계층 유동해석을 효율적으로 모사하기 위해, Reynolds-averaged Navier-Stokes Simulation기법과 Large Eddy Simulation기법의 혼합형태의 새로운 수치모형을 개발하고자 한다

A new hybrid large-eddy simulation / Reynolds-averaged Navier-Stokes simulation (LES/RANS) method is presented in this work. In this approach, the resolved turbulence kinetic energy, ensemble-averaged modeled turbulence kinetic energy and turbulence frequency, and time-resolved turbulence frequency are used to form an estimate of an outer-layer turbulence length scale that is nearly Reynolds-number independent. The ratio of this outer-layer scale with an inner-layer length scale (proportional to the wall distance) is used to construct a blending function that facilitates the shift between an unsteady RANS formulation near solid surfaces and a LES formulation away from the wall. The new model is tested through simulations of compressible flat-plate boundary layers over a wide range of Reynolds numbers and Mach 2.85 flow over a smooth compression ramp. The results show that the new model provides results for mean and second-moment statistics that are in good agreement with experiment and are comparable to those obtained using an earlier model which required a case-by-case calibration of a model constant.

Edwards et al. (2008) AIAA Journal; Choi et al. (2008) AIAA Journal; Gieseking et al. (2010) AIAA Journal

Mean velocity profies for the present hybrid LES/RANS simulation

The effect of Reynolds number on skin-friction coefficient

Vortical structures visualized using an iso-surface of swirl strength

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Fully Explicit Projection Method for Incompressible flow


본 연구는 비압축성 유체를 수치적으로 해석하기 위한 새로운 수치적 방법에 대한 내용이다. 유동에 대한 지배방정식인 Navier-Stokes equation의 continuity 조건을 만족시키기 위해 압력에 대한 Poisson equation을 풀어야 하는데, 기존의 implicit solver는 많은 계산비용이 요구된다. 이를 해결하기 위해 explicit한 방법을 모색하였다.


The Poisson equation for pressure arising from nonzero divergence of the nonlinear term in the integration of the Navier-Stokes equations requires a lot of computational cost except for cases with periodic domain. In order to mitigate this cost, we propose a new project algorithm which is fully explicit, thus not requiring iterations. The projection operator, , which projects any vector field with divergence into the divergence-free subspace in the Fourier space, when the distance from the point in question. This allows truncation so that the resulting local distribution of the projection operator, through convolution, can be used to obtain projected nonlinear terms which have relatively small divergence. This `approximate’ projection scheme was then applied to direct numerical simulation of isotropic turbulence to investigate effectiveness and efficiency of the scheme in reducing divergence and correct projection of the nonlinear terms through the statistical properties of the turbulent flow.

Test results in isotropic turbulence

Used number of coefficients:
Maximum iteration number: 3000(1sec)
Record: 600(0.2sec)
                 Correlation                                                Energy spectrum 

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