HR: 0800h
AN: H11D-1301 [Abstracts]
TI: The Comparison of Accuracy Using CIP Method and Typical Numerical Methods for One-Dimensional Solute
Transport
AU: * Kikuchi, T
EM: g236c001@edu.soft.iwate-pu.ac.jp
AF: Iwate Prefectural University, Sugo 152-52, Takizawa village, 020-0193
Japan
AU: Noborio, K
EM: noboriok@isc.meiji.ac.jp
AF: Meiji University, Higashi-mita 1-1-1, Tama-ku, Kawasaki, 214-8571
Japan
AU: Katamachi, K
EM: katamati@soft.iwate-pu.ac.jp
AF: Iwate Prefectural University, Sugo 152-52, Takizawa village, 020-0193
Japan
AU: Abe, Y
EM: yoshi@soft.iwate-pu.ac.jp
AF: Iwate Prefectural University, Sugo 152-52, Takizawa village, 020-0193
Japan
AB:
A numerical method with high accuracy to solve the CDE (convective-dispersive equation) of solute transports is described.
A coupled water-solute-heat transport model in soil was proposed by Nassar et al. (1992) and Friedel (2001). Simulation
codes based on the coupled transport model is needed. The coupled transport model is expressed non-linear system of CDEs.
Various numerical methods to solve the CDE have been developed for decades. Recently, CIP (Cubic-Interpolated
Pseudo-Particle/Propagation) method was proposed by Takewaki et al. in1985. A proper numerical method, which gives
sufficient accuracy in both cases of large dispersion and large advection, must be selected. For evaluating the accuracy of
various numerical methods, the results calculated with numerical methods have to be compared with those with an analytical
solution. The analytical solution introduced by van Genuchten and Wierenga (1986) was used in this study.
The accuracy for each numerical method was evaluated using numerical errors against the analytical solution. The value of
RMSE (Root Mean-Square Error) and the maximal value of absolute error were applied in each grid points. The numerical
methods used were the CIP method and conventional methods, i.e. the upwind scheme, the Lax-Wendroff scheme and the
Crank-Nicolson scheme.
In the case of large diffusion, the RMSE values of the CIP method, the Lax-Wendroff scheme and the Crank-Nicolson scheme were
similar, and those were 13% of the RMSE using the upwind scheme. The maximal value of error using the CIP method was 16%
of that using the upwind scheme, and 90% of that using the Lax-Wendroff and the Crank-Nicolson schemes. In the case of
large advection, the RMSE value using the CIP method was 50% of that using the Lax-Wendroff and the Crank-Nicolson schemes,
and 40% of that using the upwind scheme. The maximal value of error using the CIP method was 65% of that using the
Lax-Wendroff and the Crank-Nicolson schemes, and 90% of that using the upwind scheme.
To conclude, the CIP method was found to be useful for obtaining numeriacal solution with satisfactory accuracy in both
cases of large diffusion and large advection. The CIP method may be effective to simulate the coupled transport model, e.g.,
coupled water-solute transport and coupled water-solute-heat transport.
DE: 1849 Numerical approximations and analysis
SC: Hydrology [H]
MN: Fall Meeting 2005