Abstract: A method for treating boundary cells over a time-step in a computational fluid dynamic process employing a computational mesh representation of a fluid system characterized by governing equations and having at least one moving boundary comprises: identifying interior cells, boundary cell faces, boundary vertices, interior vertices and vertex locations at the beginning of the time step; applying a calculation process that includes determining cell volumes based on Lagrangian locations of the interior and boundary vertices and calculating the value of at least one system thermodynamic property; calculating at least one flux value across one or more boundary cell volumes by returning the interior vertices to their initial locations.

Abstract: A method and apparatus for accessing a data representation of a model associated with a fluid system, the data representation including at least one interior cell and at least one ghost cell, calculating a physical volume value and physical surface area value for at least one interior cell and at least one ghost cell, generating at least one control volume based on one or more physical volume values, generating at least one control surface based on one or more physical surface area values; substituting one or more of the at least one control volume parameter and the at least one surface area for corresponding elements of mathematical conservation equations representative of the fluid system, and solving the mathematical conservation equations representative of the fluid system.