An upwind-based scheme for solving the oblique derivative boundary-value problem related to physical geodesy

Abstract

The paper presents a novel original upwindbased approach for solving the oblique derivative boundary value problem by the finite volume method. In this approach, the oblique derivative boundary condition is interpreted as a stationary advection equation for the unknown disturbing potential. Its approximation is then performed by using the first order upwind scheme taking into account information from inflow parts of the finite volume boundary only. When the numerical scheme is derived, numerical simulations in 2D and 3D domains are performed and the experimental order of convergence of the proposed algorithm is studied. Moreover a comparison with a solution by the central scheme previously used for this kind of problem is performed. Finally we present numerical experiments dealing with the global and local gravity field modelling.

Keywords

• Finite volume method
• Oblique derivative boundary-value problem
• Upwind principle