An analysis of the numerical solution of the transport equation
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Various finite difference and finite element methods for solving the one‐dimensional convective‐dispersive equation are investigated. A Fourier series analysis is performed to determine the dissipative and dispersive characteristics of these numerical methods. The analysis indicates that the commonly observed phenomenon of overshoot of a concentration pulse is due to the inability of the numerical schemes to propagate the small wavelengths which are important to the description of the front. Furthermore, the numerical smearing of a sharp front is due to dissipation of these small wavelengths. The finite element method was found to be superior to finite difference methods for solution of the convective‐dispersive equation.
Transport Equation, One‐Dimensional, Convective‐Dispersive Equation
G. Gray, William and F. Pinder, George, "An analysis of the numerical solution of the transport equation" (1976). KIP Articles. 196.