• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2007.05a
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• pp.170-175
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• 2007

The finite volume method for forging simulation is examined to reveal its possibility as well as its problem in this paper. For this study, the finite volume method based MSC/SuperForge and the finite element method based AFDEX are employed. The simulated results of the homogeneous compression obtained by the two softwares are compared to indicate the problems of the finite volume method while several application examples are given to show the possibility of the finite volume method for simulation of upsetter forging processes. It is shown that the finite volume method can not predict the exact solution of the homogeneous compression especially in terms of forming load and deformed shape but that it is helpful to simulate very complex forging processes which can hardly be simulated by the conventional finite element method.

• Coupled systems mechanics
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• v.9 no.1
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• pp.5-28
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• 2020

Despite a widely-held belief that the finite element method is the method for the solution of solid mechanics problems, which has for 30 years dissuaded solid mechanics scientists from paying any attention to the finite volume method, it is argued that finite volume methods can be a viable alternative. It is shown that it is simple to understand and implement, strongly conservative, memory efficient, and directly applicable to nonlinear problems. A number of examples are presented and, when available, comparison with finite element methods is made, showing that finite volume methods can be not only equal to, but outperform finite element methods for many applications.

• Transactions of Materials Processing
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• v.16 no.3 s.93
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• pp.187-192
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• 2007

The finite volume method for forging simulation is examined to reveal its possibility as well as its problem in this paper. For this study, the finite volume method based MSC/SuperForge and the finite element method based AFDEX are employed. The simulated results of the homogeneous compression obtained by the two softwares are compared to indicate the problems of the finite volume method while several application examples are given to show the possibility of the finite volume method fur simulation of complex hot forging processes. It is shown that the finite volume method can not predict the exact solution of the homogeneous compression especially in terms of forming load and deformed shape but that it is helpful to simulate very complex forging processes which can hardly be simulated by the conventional finite element method.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.1565-1568
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• 2003

The backward extrusion process is one of the commonly used metal forming processes. In this paper. a battery case which has the rectangular section, is analyzed using a 3D metal forming package(MSC.Superforge). This pacakge uses the finite volume analysis method. It is shown that the MSC.Superforge package using finite volume method provides result very close to those obtained from a finite element analysis package(MSC.Superform). However, the simulation time using the finite volume method was almost 10 % of the simulation time consumed by the other package using finite element method. Moreover, the finite volume method used in MSC.Superforge can eliminate the remeshing problems that make the simulating a metal forming process with severe deformation, such as the extrusion process, so difficult.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1205-1219
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• 2011

In this work, a stabilized characteristic finite volume method for the time-dependent Navier-Stokes equations is investigated based on the lowest equal-order finite element pair. The temporal differentiation and advection term are dealt with by characteristic scheme. Stability of the numerical solution is derived under some regularity assumptions. Optimal error estimates of the velocity and pressure are obtained by using the relationship between the finite volume and finite element methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.4
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• pp.249-260
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• 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
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• v.12 no.2
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• pp.69-79
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• 2008

Multigrid methods finite element/finite volume methods and their convergence properties are reviewed in a general setting. Some early theoretical results in simple finite element methods in variational setting method are given and extension to nonnested-noninherited forms are presented. Finally, the parallel theory for nonconforming element[13] and for cell centered finite difference methods [15, 23] are discussed.

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

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2003.05a
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• pp.461-464
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• 2003

A new control volume finite element method is proposed for three dimensional analysis of polymer flow. Tetrahedral finite element is employed and co-located interpolation procedure for pressure and velocity is implemented. Inclusion of pressure gradient term in the velocity shape functions prevents the checkerboard pressure field from being developed. Vectorial nature of pressure gradient is considered in the velocity shape function so that velocity profile in the limit of very small Reynolds number becomes physically meaningful. The proposed method was verified through three dimensional simulation of pipe flow problem for Newtonian and power-law fluid. Calculated pressure and velocity field showed an excellent agreement with analytic solutions for pressure and velocity. Driven-cavity problem, which is reported to yield checkerboard pressure filed when conventional finite element method is applied, could be solved without yielding checkerboard pressure field when the proposed control volume finite element method was applied. The proposed method could be successfully applied to the three dimensional mold filling problem.

• 한국전산유체공학회:학술대회논문집
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• 2009.11a
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• pp.228-230
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• 2009

The moment-of-fluid (MOF) method is a new volume-tracking method that accurately treats evolving material interfaces. Based on the moment data (volume and centroid) for each material, the material interfaces are reconstructed with second-order spatial accuracy in a strictly conservative manner. The MOF method is coupled with a stabilized finite element incompressible Navier-Stokes solver for two fluids, namely water and air. The effectiveness of the MOF method is demonstrated with a free-surface dam-break problem.