Finite Element Modelling of the Hydrodynamic Environment of a Small ROV

Abstract

This paper addresses a practical problem, namely, modeling the hydrodynamic environment of a small ROV. This has become the problem of solving time-dependent incompressible Navier-Stokes equations with moving boundaries and a new method is developed to solve it. Navier-Stokes equations expressed in a moving-body-fixed coordinate frame with moving boundaries are derived and solved by a proposed finite element method which is a modified velocity correction procedure (Ren and Utnes 1993). The present method is implemented in the C language on a SUN/Sparc Station. The algorithm and program are demonstrated by solving a classic driven cavity flow problem and a simplified model of the hydrodynamic environment of a small ROV, which is a moving boundary problem. The results from the driven cavity flow problem are compared to previous work. A definition is also given of the moving boundary problem (MBP) related to the solution of Navier-Stokes equations.

Keywords

• Moving boundary
• finite element
• hydrodynamic model