A COMPARISON OF INTEGRATION AND INTERPOLATION EULERIAN-LAGRANGIAN METHODS

Selected finite element Eulerian-Lagrangian methods for the solution o f the transport equation are compared systematically in the relatively simple context of 1D, constant coefficient, conservative problems. A combination of formal analysis and numerical experimentation is used t o characterize the stability and accuracy that results from alternativ e treatments of the concentrations at the feet of the characteristic l ines. Within the methods analyzed, those that approach such treatment with the perspective of 'integration' rather than 'interpolation' tend to have superior accuracy. Exact integration leads to unconditional s tability and excellent accuracy. Quadrature integration leads only to conditional stability, but newly derived criteria show that stability restrictions are relatively mild and should not preclude the usefulnes s of quadrature integration methods in a range of practical applicatio ns. While conclusions cannot be extended directly to multiple dimensio ns and complex flows and geometries, results should provide useful ins ight to the development and behaviour of specific Eulerian-Lagrangian transport models.