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. Author manuscript; available in PMC: 2015 Oct 1.

Published in final edited form as: J Comput Phys. 2014 Oct 1;274:95–121. doi: 10.1016/j.jcp.2014.06.003

Plots of density, magnitude of the error in velocity and pressure, and volume fraction for the isolated interface advection problem given by Eq. (34). The exact solution (—), along with three numerical solutions distinguished by the type and order of accuracy of the cell average variables that are reconstructed at the cell boundaries, are compared at t = 200. The latter include the conservative variables ( ), the second-order accurate primitive variables ( ), following Johnsen and Colonius [30], and the fourth-order accurate primitive variables ( ), following the present numerical scheme.

Inline graphic — Plots of density, magnitude of the error in velocity and pressure, and volume fraction for the isolated interface advection problem given by Eq. (34). The exact solution (—), along with three numerical solutions distinguished by the type and order of accuracy of the cell average variables that are reconstructed at the cell boundaries, are compared at t = 200. The latter include the conservative variables ( ), the second-order accurate primitive variables ( ), following Johnsen and Colonius [30], and the fourth-order accurate primitive variables ( ), following the present numerical scheme.