• Journal of the Korea Computer Graphics Society
• /
• v.25 no.5
• /
• pp.21-30
• /
• 2019

We propose a physical simulation method based on the shallow water equation(SWE) to represent water surface effectively. In this paper, the water which can be represented has a much larger width compared to the depth does not have a large vertical direction flow. In order to calculate the water flow efficiently, we start with the shallow water equation as the governing equation, which is a simplified version of the Navier-Stokes equation. In order to numerically calculate the advection term of the SWE, we introduce a new conservtive USCIP(CUSCIP) method which improves the Constrained Interpolation Profile (CIP) method to preserve the physical quantity while increasing the numerical accuracy. The proposed method is based on Kim et. al.'s Unsplit Semi-lagrangian CIP[9], and calculates advection term with additional constraints on term that consider integral values. The experimental results show that the CUSCIP method is robust to the loss of physical quantity due to numerical dissipation, which improves wave detail and persistence.

• Journal of Korea Water Resources Association
• /
• v.45 no.2
• /
• pp.179-189
• /
• 2012

To simulate the transport of pollutant, a numeric model for the advection-diffusion equation with the decay term is developed. This is finite-difference model using the implicit method (with the weight factor ${\alpha}$) and Gauss-Seidel SOR(successive over-relaxation). This model is compared to the analytical solutions (of simpler dimensional or boundary conditions), and in the condition of Peclet number < 5~20, the result shows stable condition, and Crank-Nicolson method (${\alpha}$=0.5) shows the more accurate results than fully-implicit method (${\alpha}$=1). The mass of advection, diffusion and decay is calculated and the error of mass balance is less than 3%. This model can evaluate the 3-D concentrations of the advection-diffusion and decay problems, but this model uses only the finite-difference method with the fixd grid system, so it can be effectively used in the problems with small Peclet numbers like the pollutant transport in groundwater.

• Water for future
• /
• v.28 no.4
• /
• pp.125-136
• /
• 1995

ELM, a characteristic line based method, was applied to advection-dispersion equation, and the results obtained were compared with those of Eulerian schemes(Stone-Brian and QUICKEST). The calculation methods consisted of Lagrangian interpolation scheme and cubic spline interpolation scheme for the advection calculation, and the Crank-Nicholson scheme for the dispersion calculation. The results of numerical methods were as follows: (1) for Gaussian hill: ELM, using Lagrangian interpolation scheme, gave the most accurate computational result, ELM, using cubic spline interpolation scheme, and QUICKEST scheme gave numerical damping for Peclet number 50. Stone-Brian scheme gave phase shift introduced in the numerical solution for Peclet number 10 and 50. (2) for advanced front: All schemes gave accurate computational results for Peclet number 1 and 4. ELM, Lagrangian interpolation scheme, and Stone,Brian scheme gave dissipation error and ELM, using cubic spline interpolation scheme, and QUICKEST scheme gave numerical oscillation for Peclet number 50.

• Journal of Korea Water Resources Association
• /
• v.30 no.2
• /
• pp.143-154
• /
• 1997

A numerical model for solving advection-diffusion equation is presented by splitoperator method combining the Holly-Preissmann scheme with a fifth-degree interpolating polynomial for advection operator and the explicit scheme porposed by Hobson et al. for diffusion operator. To examine the developed model, the obtained numerical solutions are compared with both the analytic solution and those from the existing models for the instantaneous source (Gaussian hill) and the continuous source (advanced front) at upstream boundary with constant velocity and diffusivity condition. For the various cases having different Courant and Peclet numbers, it is shown that the present study provides stable solutions even for Courant numbers exceeding one. The result obtained by the present study also agree well with existing analytical solutions for both cases. The proposed explicit scheme somewhat releases the conventional restriction of explicit schemes for determining the time step size and provides satisfactory results for relatively large time step size.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.26 no.2B
• /
• pp.171-178
• /
• 2006

The finite element model based on the 2-D advection-dispersion equation incorporating the dispersion tensor that is calculated using velocity field data was developed in order to analyze more accurately 2-D mixing of pollutants for meandering streams. The proposed model was tested using the straight channel that inclined at 45o in the Cartesian coordinate system. The simulation results showed that dispersion tensor model using velocity field data gives an accurate solution. The suitability of the proposed model in analyzing actual pollutant mixing in meandering channels was demonstrated by comparing the simulation results with experimental data obtained from the tracer tests in the laboratory flume. Comparison results showed that the proposed model with dispersion tensor can represents more accurately the mixing phenomena of the pollutants in the meandering channels in which the direction of the primary flow is varying periodically along the channel.

• Journal of the Korea Computer Graphics Society
• /
• v.15 no.1
• /
• pp.1-6
• /
• 2009

This paper presents a new CIP method for unstructured mesh to reduce the numerical dissipation. To reflect precise physical characteristics, CIP method updates both the physical quantity and the derivative information. The proposed method uses the Finite Volume Method(FVM) to solve the non-advection term of CIP equation. And we performed several experiments to improve the accuracy of third-order interpolation. Our result shows that our algorithm has less numerical dissipation than that of linear advection solver.

• Journal of Environmental Science International
• /
• v.11 no.12
• /
• pp.1321-1326
• /
• 2002

A numerical model is investigated to predict a behavior of the gaseous volatile organic compounds and a subsurface contamination caused by them in the unsaturated zone. Two dimensional advective-dispersion equation caused by a density difference and two dimensional diffusion equation are computed by a finite difference method in the numerical model. A laboratory experiment is also carried out to compare the results of the numerical model. The dimensions of the experimental plume are 1.2m in length, 0.5m in height, and 0.05m in thickness. In comparing the result of 2 methods used in the numerical model with the one of the experiment respectively, the one of the advective-dispersion equation shows better than the one the diffusion equation.

• Journal of Korea Water Resources Association
• /
• v.45 no.5
• /
• pp.473-480
• /
• 2012

A two-dimensional depth-integrated hydrodynamic and a depth-averaged passive scalar transport models were developed by using a Compact Finite Volume Method (CFVM) which can assure a higher order accuracy. A typical wave current interaction experimental data set was compared with the computed results by the proposed CFVM model, and resonable agreements were observed from the comparisons. One and two dimensional scalar advection tests were conducted, and very close agreements were observed with very little numerical diffusion. Finally, a turbulent mixing simulation was done in an open channel flow, and a reasonable similarity with LES data was observed.

• Journal of Korea Water Resources Association
• /
• v.34 no.2
• /
• pp.177-186
• /
• 2001

By using he total variation diminishing (TVD) condition, accurate and upwind based schemes are firstly introduced to develop numerical models free from nonphysical oscillations in the vicinity of large gradients. These models are then applied to both abruptly and smoothly varying initial conditions. By comparing computed predictions to analytical solutions, it is clearly shown that the first-order upwind scheme produces the numerical viscosity and the second-order Lax-Wendroff scheme produces the spurious oscillations. However, the TVD scheme gives the most reasonable results.

• 한국전산유체공학회:학술대회논문집
• /
• 2009.11a
• /
• pp.223-227
• /
• 2009

In the present study, a least square weighted residual method and Taylor-Galerkin method were formulated and tested for the discretization of the two hyperbolic type equations of level set method; advection and reinitialization equations. The two approaches were compared by solving a time reversed vortex flow and three-dimensional broken dam flow by employing a four-step splitting finite element method for the solution of the incompressible Navier-Stokes equations. From the numerical experiments, it was shown that the least square method is more accurate and conservative than Taylor-Galerkin method and both methods are approximately first order accurate when both advection and reinitialization phase are involved in the evolution of free surface.