In the numerical modeling of groundwater solute transport, explicit solutions may be obtained for the concentration field at any future time without computing concentrations at intermediate times. The spatial variables are discretized and time is left continuous inthe governing differnetial equation. These semianalytical solutions have been presented in the literature and involve the eigensystem of a coefficient matrix. This eigensystem may be complex (i. e. , have imaginary components) due to the asymmetry created by the advection term in the governing advection-dispersionequation. It is shown here that the error due to ignoring the imaginary components of complex eigenvalues is large for small dispersivity values. A new algorithm that represents the complex eigensystem by converting it to a real eigensystem is presented. The method requires only real arithmetic.
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PROBLEM OF COMPLEX EIGENSYSTEMS INTHE SEMIANALYTICAL SOLUTION FOR ADVANCEMENT OF TIME IN SOLUTE TRANSPORT SIMULATIONS: A NEW METHOD USING REAL ARITHMETIC.