Theses and Dissertations

Issuing Body

Mississippi State University


Whitfield, David L.

Committee Member

Marcum, David L.

Committee Member

Briley, W. Roger

Committee Member

Taylor, Lafayette K.

Committee Member

Sreenivas, Kidambi

Date of Degree


Original embargo terms

MSU Only Indefinitely

Document Type

Dissertation - Campus Access Only


Aerospace Engineering

Degree Name

Doctor of Philosophy


College of Engineering


Department of Aerospace Engineering


Of the surface capturing schemes, the levelset and multi-phase models are implemented and extensively examined. First, the levelset method is shown, and its weaknesses are identified; a mis- appropriation of changes in momentum, a strong dependence on the density by the eigenvalues of the inviscid flux Jacobian, and a prescribed density transition. These weaknesses are specifically addressed and overcome by the formulation of the multi-phase model. Consequently, the multi-phase model is chosen for this work. Previous surface fitting techniques simply absorb the gravitational source term into the pressure. It must be noted that this absorbtion is valid only for single density flows; since the surface fitting approach is solving only one side of the interface, there is no significant change in the density througout the domain. Consequently, absorbing the gravitational source into the pressure term is not possible in a surface capturing scheme in which both sides of the interface are solved. Thus, a new treatment of the gravitational source term is required and is presented in this work. A multi-phase model is implemented into a parallel, three-dimensional, unsteady, incompressible Navier-Stokes flow solver for the purpose of examining free surface flows on unstructured meshes. The reasons for choosing this model above others are presented, and the multi-phase model is discussed. The base algorithm is briefly examined with emphasis given to the areas which require additional care. The construction of the gravity source term which drives the formation of the waves is explained in detail, and its effects on the rest of the algorithm are identified. Finally, the method is carefully compared with available data on a submerged NACA 0012 airfoil, the Wigley Hull, the Series 60 Cb=0.6 ship, and the DTMB 5415 ship.