A projection method for constructing a mass conservative velocity field Original Research Article

In the numerical modeling of fluid flow and transport problems, the velocity field frequently needs to be projected from one finite dimensional space into another. In certain applications, especially those involving modeling of multi-species transport, the new projected velocity field should be accurate as well as locally mass conservative. In this paper, a velocity projection method has been developed that is both accurate and mass conservative element-by-element on the projected grid. The velocity correction is expressed as gradient of a scalar pressure field, and the resultant Poisson equation is solved using a mixed/hybrid finite element method and lowest-order Raviart-Thomas spaces. The conservative projection method is applied to the system of shallow water equations and a theoretical error estimate is derived.