Abstract
Most of the numerical schemes commonly used for solving the scalar advection equation are not simultaneously: positive definite, high accurate, mass conserving and monotone. Semi Lagrangian numerical schemes derived by van Leer [1977a, b] and Colella and Woodward [1984], which were developed for compressible flow problems, seem to have the potential in fulfilling these conditions, all at the same time. In order to assess their qualities for the scalar advection problems, three of the most accurate schemes have been selected and subjected to some standard test cases. The test results are compared with the test results obtained for two well known numerical schemes: the Second Moment Method (SMM) (Egan and Mahoney [1972]) and the Multidimensional Flux Corrected Transport (MFCT) (Zalesak [1979], [1981]). Before discussing the test results, the schemes are derived following a generalized approach.
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