• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2007.04a
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• pp.30-33
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• 2007

DSMC method is now widely accepted CFD approach to compute and simulate the nozzle plume in rarefied regimes. In this study, using SMILE(Statistical Modeling in Low-density Environment) code which was developed in ITAM, Russia and coded using DSMC method, the internal flow of the Rothe micronozzle was simulated. Moreover, to show the validity of the SMILE code, the centerline temperatures according to the Reynold's number were compared with the ones obtained by the Rothe's experiment.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.745-756
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• 2022

We study a nonlinear wave equation on finite connected weighted graphs. Using Rothe's and energy methods, we prove the existence and uniqueness of solution under certain assumption. For linear wave equation on graphs, Lin and Xie [10] obtained the existence and uniqueness of solution. The main novelty of this paper is that the wave equation we considered has the nonlinear damping term |u_t|^p-1·u_t (p > 1).

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1179-1192
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• 2012

In this paper, we consider a doubly nonlinear parabolic partial differential equation $\frac{{\partial}{\beta}(u)}{{\partial}t}-{\Delta}_pu+f(x,t,u)=0$ in ${\Omega}{\times}[0,T]$, with Dirichlet boundary condition and initial data given. We prove the existence of a discrete approximate solution by means of the Rothe discretization in time method under some conditions on ${\beta}$, $f$ and $p$.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.2
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• pp.1-11
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• 2002

In the present study, a parallel DSCM technique based on a cell-based data structure is developed for the efficient simulation of rarefied gas flows especially od PC clusters. Dynamic load balancing is archieved by decomposing the computational domain into several sub-domains and accounting for the number of particles and the number cells of each domain. Mesh adaptation algorithm is also applied to improve the resolution of the solution and to reduce the grid dependency. It was demonstrated that accurate solutions can be obtained after several levels of mesh adapation starting from a coars initial grid. The method was applied to a two-dimensioanal supersonic leading-edge flow and the axi-symmetric Rothe nozzle flow to validate the efficiency of the present method. It was found that the present method is a very effective tool for the efficient simulation of rarefied gas flow on PC-based parallel machines.