• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.4
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• pp.291-306
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• 2011

We consider the second order Strang splitting method to approximate the solution to the KdV equation. The model equation is split into three sets of initial value problems containing convection and dispersal terms separately. TVD MUSCL or MUSCL scheme is applied to approximate the convection term and the second order centered difference method to approximate the dispersal term. In time stepping, explicit third order Runge-Kutta method is used to the equation containing convection term and implicit Crank-Nicolson method to the equation containing dispersal term to reduce the CFL restriction. Several numerical examples of weakly and strongly dispersive problems, which produce solitons or dispersive shock waves, or may show instabilities of the solution, are presented.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.10 no.4
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• pp.237-246
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• 2012

In this study, numerical model for transport of radionuclide and colloid was developed. In order to solve reaction-migration governing equation for colloid and radionuclide, Strang-splitting Sequential Non-Iterative (SNI), which is one of Operator Splitting Method, was used for numerical method and this was coded by MATLAB. From the verification by comparing the simulation results with analytical solution considering only solute transport and rock diffusion, the Pearson's correlation coefficient was greater than 0.99 which demonstrates the accuracy of the model.

• Journal of The Korean Astronomical Society
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• v.28 no.2
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• pp.223-243
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• 1995

We describe the implementation of a multi-dimensional numerical code to solve the equations for idea! magnetohydrodynamics (MHD) in cylindrical geometry. It is based on an explicit finite difference scheme on an Eulerian grid, called the Total Variation Diminishing (TVD) scheme, which is a second-order-accurate extension of the Roe-type upwind scheme. Multiple spatial dimensions are treated through a Strang-type operator splitting. Curvature and source terms are included in a way to insure the formal accuracy of the code to be second order. The constraint of a divergence-free magnetic field is enforced exactly by adding a correction, which involves solving a Poisson equation. The Fourier Analysis and Cyclic Reduction (FACR) method is employed to solve it. Results from a set of tests show that the code handles flows in cylindrical geometry successfully and resolves strong shocks within two to four computational cells. The advantages and limitations of the code are discussed.