• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.12 no.4
• /
• pp.249-260
• /
• 2008

In this work we propose a mixed finite volume method for the Signorini problem which are based on the idea of Keller's finite volume box method. The triangulation may consist of both triangles and quadrilaterals. We choose the first-order nonconforming space for the scalar approximation and the lowest-order Raviart-Thomas vector space for the vector approximation. It will be shown that our mixed finite volume method is equivalent to the standard nonconforming finite element method for the scalar variable with a slightly modified right-hand side, which are crucially used in a priori error analysis.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.5 no.1
• /
• pp.55-78
• /
• 2001

Given the anisotropic Poisson equation $-{\nabla}{\cdot}{\mathcal{K}}{\nabla}p=f$, one can convert it into a system of two first order PDEs: the Darcy law for the flux $u=-{\mathcal{K}{\nabla}p$ and conservation of mass ${\nabla}{\cdot}u=f$. A very natural mixed finite volume method for this system is to seek the pressure in the nonconforming P1 space and the Darcy velocity in the lowest order Raviart-Thomas space. The equations for these variables are obtained by integrating the two first order systems over the triangular volumes. In this paper we show that such a method is really a standard finite element method with local recovery of the flux in disguise. As a consequence, we compare two approaches in analyzing finite volume methods (FVM) and shed light on the proper way of analyzing non co-volume type of FVM. Numerical results for Dirichlet and Neumann problems are included.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.3 no.6
• /
• pp.112-122
• /
• 1995

As an alternative fuel producing less exhaust emissions, natural gas is of interest for use both in SI and CI engines. The potential of natural gas fuelled dual-fuel engine is considered high enough. However, much effort has to be made so that gaseous fuel is used efficiently with simultaneous minimum use of pilot oil. Hence, a simplified three-dimensional model, using a finite volume method in cylindrical coordinates, has been developed to facilitate an understanding of the dual-fuel combustion phenomena and to predict the complex interactions between the pilot distillate and natural gas. The computer model was calibrated by comparing it with the experimental results obtained from diesel engine like combustion bomb tests. In the pre-mixed natural gas combustion, the fuel burning was highly reliant on the injection condition and subsequent burning nature of the pilot distillate.

• Journal of Power System Engineering
• /
• v.13 no.5
• /
• pp.11-17
• /
• 2009

A numerical study of unsteady mixed convection in a cavity with high viscous fluid is presented. Finite volume method was employed for the discretization and PISO algorithm was used for calculating pressure term. The parameters governing the problem are the Rayleigh number ($10^3\;{\leq}\;Ra\;{\leq}\;10^5$), the Reynolds number (0 < Re $\leq$ 1), and the aspect ratio (0.5 $\leq$ AR $\leq$ 2). The fluid used is silicon oil, a high prandtl number fluid, Pr = 909.1. The results show velocity vectors and temperature distributions. It is found that the periodic flows in a cavity are observed at very low Reynolds numbers, and the period of periodic flow decreases with increasing Reynolds and Rayleigh numbers, and increases with increasing aspect ratio. Also, the Reynolds number range of periodic flow increases with increasing Rayleigh numbers and aspect ratio.

• Journal of the Korean Mathematical Society
• /
• v.59 no.3
• /
• pp.519-548
• /
• 2022

In this paper, a stabilized-penalized collocated finite volume (SPCFV) scheme is developed and studied for the stationary generalized Navier-Stokes equations with mixed Dirichlet-traction boundary conditions modelling an incompressible biological fluid flow. This method is based on the lowest order approximation (piecewise constants) for both velocity and pressure unknowns. The stabilization-penalization is performed by adding discrete pressure terms to the approximate formulation. These simultaneously involve discrete jump pressures through the interior volume-boundaries and discrete pressures of volumes on the domain boundary. Stability, existence and uniqueness of discrete solutions are established. Moreover, a convergence analysis of the nonlinear solver is also provided. Numerical results from model tests are performed to demonstrate the stability, optimal convergence in the usual L² and discrete H¹ norms as well as robustness of the proposed scheme with respect to the choice of the given traction vector.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
• /
• v.13 no.12
• /
• pp.1230-1235
• /
• 2001

The laminar convection heat transfer in a ventilated space with various horizontal partitions was studied numerically and experimentally. The experimental results by holographic interferometer showed good agreements with the numerical results. For the numerical study, the governing equations were solved by using a finite volume method for $46.6\leqRe\leq1332,\;1460\leqGr\leql1585$, Pr=0.71 and the variations of partition lengths. The isotherms and velocity vectors have been represented for various parameters. As the length of partition increases, the convection heat transfer decreases. Based on the numerical data, a correlation was obtained for the dimensionless mean Nusselt number in terms of $Gr/Re^2$. In the region of $Gr/Re^2$<1, the mean Nusselt number was very small, but in the region of $Gr/Re^2\geq1$, the mean Nusselt number was constant.

• Journal of the Korean Society of Industry Convergence
• /
• v.3 no.4
• /
• pp.329-336
• /
• 2000

A geometric and material nonlinear finite element analysis is developed for the layered elastomeric bearings. In this study, a mixed variational approach with separate variables is used to describe the displacement and volume change of rubber. To represent finely deformed behavior, Kirchoff stress tensors are used and converted Eulerian stress tensors to describe real physical meanings. Newton's method is utilized to solve the governing nonlinear finite element equations. Numerical test are performed in the case of compression and shear to verify the theory and to illustrate the application of this analysis. And the results of this study were compared to the results of Moore's discrete finite element analysis.

• Journal of Mechanical Science and Technology
• /
• v.18 no.6
• /
• pp.1026-1035
• /
• 2004

An immersed boundary method for solving the Navier-Stokes and thermal energy equations is developed to compute the heat transfer over or inside the complex geometries in the Cartesian or cylindrical coordinates by introducing the momentum forcing, mass source/sink, and heat source/sink. The present method is based on the finite volume approach on a staggered mesh together with a fractional step method. The method of applying the momentum forcing and mass source/sink to satisfy the no-slip condition on the body surface is explained in detail in Kim, Kim and Choi (2001, Journal of Computational Physics). In this paper, the heat source/sink is introduced on the body surface or inside the body to satisfy the iso-thermal or iso-heat-flux condition on the immersed boundary. The present method is applied to three different problems : forced convection around a circular cylinder, mixed convection around a pair of circular cylinders, and forced convection around a main cylinder with a secondary small cylinder. The results show good agreements with those obtained by previous experiments and numerical simulations, verifying the accuracy of the present method.

• Journal of the Korean Society of Manufacturing Process Engineers
• /
• v.21 no.9
• /
• pp.85-91
• /
• 2022

The demand for electric vehicles has increased because of environmental regulations. The lithium-ion battery, the most widely used type of battery in electric vehicles, is composed of a cathode, an anode, and an electrolyte. It is manufactured according to the pole plate, assembly, and formation processes. To improve battery performance and increase manufacturing efficiency, the manufacturing process must be optimized. To do so, simulation can be used to reduce wasted resources and time, and a finite-element method can be utilized. For high simulation quality, it is essential to reflect the material properties of the electrode by considering the pores. However, the material properties of electrodes are difficult to derive through measurement. In this study, the representative volume element method, which is a homogenization method, was applied to estimate the representative material properties of the electrode considering the pores. The representative volume element method assumes that the strain energy before and after the conversion into a representative volume is conserved. The method can be converted into one representative property, even when nonhomogeneous materials are mixed in a unit volume. In this study, the material properties of the electrode considering the pores were derived. The results should be helpful in optimizing the electrode manufacturing process and related element technologies.

• Journal of Korea Water Resources Association
• /
• v.44 no.2
• /
• pp.109-123
• /
• 2011

In this study, 2D finite volume model, which can apply to the mixed meshes that is effective to treat the complicated topography such as a natural river, is developed. To do so, an algorithm for finding the neighbouring cell of a computational cell is introduced, and fluxes are computed using the HLLC approximate Riemann solver at each interface between a computational cell and it's neighbouring cells. Moreover, in order to numerically treat the bed slope which has important effect on the balance between flux gradients and sourte terms, different formula to compute the bed slope for rectangular and triangular mesh are applied. The developed model is applied to analyze dam-break in an experimental channel with $90^{\circ}$ bend and Malpasset dam-break in France. The two cases consist of mixed meshes and the suggested method is validated for the experimental channel and natural channel by comparison with the experimental data, field data and computed results.