“…(7), t/, V, and W are contravariant velocity components written without metric normalization. Here, the Cartesian derivatives are expanded in £, r;, f space via chain-rule relations such as (8) Finally, the metric terms are obtained from chain-rule expansion of *£, y^ etc., and solved for £ x , % y , etc., to give (9a) (10) Several numerical schemes have been developed to solve Eq. (5).…”