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A local level set method based on a finite element method for unstructured meshes
Long Cu Ngo,최형권 대한기계학회 2016 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.30 No.12
A local level set method for unstructured meshes has been implemented by using a finite element method. A least-square weighted residual method was employed for implicit discretization to solve the level set advection equation. By contrast, a direct re-initialization method, which is directly applicable to the local level set method for unstructured meshes, was adopted to re-correct the level set function to become a signed distance function after advection. The proposed algorithm was constructed such that the advection and direct reinitialization steps were conducted only for nodes inside the narrow band around the interface. Therefore, in the advection step, the Gauss–Seidel method was used to update the level set function using a node-by-node solution method. Some benchmark problems were solved by using the present local level set method. Numerical results have shown that the proposed algorithm is accurate and efficient in terms of computational time.
Evaluation of pressure and viscous drags of a rising bubble at small Reynolds numbers
Long Cu Ngo,Hyoung Gwon Choi 대한기계학회 2022 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.36 No.3
Pressure and viscous drags acting on a bubble rising in a viscous fluid are numerically estimated to obtain the corresponding drag coefficients that are rarely reported in the existing papers. The numerical method has been successfully validated by solving the existing benchmark problems of a bubble rising in a quiescent liquid at various flow regimes. For spherical cap bubbles, the formula of total drag coefficient is proposed in a similar form to that by viscous potential flow theory expressed by the Reynolds number, and the corresponding formulas for pressure and viscous drag coefficients are derived. Furthermore, the effect of the density ratio of a bubble and the surrounding liquid on terminal velocity is also investigated for fixed Morton and Eotvos numbers: the lighter bubble has a higher terminal velocity having an asymptotic value as the density ratio increases although the Reynolds numbers based on the terminal velocity are nearly constant.
A coupled level set/volume of fluid method for simulation of two-phase flow on unstructured grids
Long Cu Ngo,Hyoung Gwon Choi,장경식 대한기계학회 2021 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.35 No.2
We present a fully coupled level set and volume of fluid method for free surface flow simulations on unstructured grids in two- and three-dimensions. The evolution of the level set function and the volume fraction are updated at each time step. The level set advection equation is solved by a least squares weighted residual method while the volume fraction advection is solved using an unsplit Eulerian-Lagrangian scheme. The reconstruction of the interface in the volume of fluid method is performed using the volume fraction information together with the normal vector obtained from the level set function. The reconstructed interface is then used to reinitialize the level set function. Thanks to the fully coupling of the two methods, the interface reconstruction is carried out efficiently and the mass conservation is preserved exactly. The proposed method is validated against several benchmarks and is coupled with the incompressible Navier-Stokes solver to solve two-phase flow problems. Numerical results show that the method is capable of resolving complex interface changes efficiently and accurately.
Ngo, Long Cu,Choi, Hyoung Gwon Elsevier 2020 COMPUTERS & MATHEMATICS WITH APPLICATIONS - Vol.79 No.4
<P><B>Abstract</B></P> <P>A multi-level adaptive mesh refinement technique for an integrated finite element/level set formulation was implemented to simulate the incompressible interfacial flows with surface tension by using unstructured P2P1 triangular and tetrahedral meshes. Linear/quadratic elements near the interface were dynamically refined as an interface evolves in order to produce an accurate solution with a lower computational cost. An adaptive mesh refinement algorithm for a linear element has been extended to a quadratic element by using a node-reordering. The proposed algorithm was successfully validated by solving several benchmark problems. Simulation of a static bubble problem was found to give an accurate solution with negligible spurious currents compared with existing results. Simulation results of rising bubble problems in 2D and 3D were also compared against existing numerical and experimental results in terms of terminal rising speed and terminal bubble shape. We have found that the present algorithm provided stable and accurate solutions even for a high density-ratio and that the solution accuracy strongly depended on the mesh resolution near the interface. Further, the present algorithm was shown to be very efficient because the computational overhead by mesh-refinement algorithm was very small compared to the elapsed times consumed for solving the incompressible Navier–Stokes equations and the advection/re-initialization equations of level set method. Lastly, the coalescence scenario of two oblique bubbles was well reproduced by the present 3D simulation.</P>
Long Cu Ngo,Hyoung Gwon Choi(최형권) 대한기계학회 2016 대한기계학회 춘추학술대회 Vol.2016 No.12
A new adaptive mesh refinement technique for P2P1 unstructured triangular meshes is proposed to simulate incompressible multiphase flow with surface tension effects. A P2P2 element is adopted to solve the governing equations of the incompressible flow and a P2-iso-P1 to solve the level set equation to capture the interface movement. The reinitialization of the level set function is performed by employing a direct approach for nodes inside the narrow band around the interface to reduce the computational time. The semi-implicit implementation of the consistent surface tension force model is carried out for the treatment of surface tension across the interface. The numerical method is validated against benchmark problems of the static bubble and rising bubble including topology changes.