FVM approach for solving the oblique derivative BVP on unstructured meshes above the real Earth’s topography

We present local gravity field modelling based on a numerical solution of the oblique derivative bondary value problem (BVP). We have developed a finite volume method (FVM) for the Laplace equation with the Dirichlet and oblique derivative boundary condition, which is considered on a 3D unstructured mesh about the real Earth’s topography. The oblique derivative boundary condition prescribed on the Earth’s surface as a bottom boundary is split into its normal and tangential components. The normal component directly appears in the flux balance on control volumes touching the domain boundary, and tangential components are managed as an advection term on the boundary. The advection term is stabilised using a vanishing boundary diffusion term. The convergence rate, analysis and theoretical rates of the method are presented in [1].

Using proposed method we present local gravity field modelling in the area of Slovakia using terrestrial gravimetric measurements. On the upper boundary, the FVM solution is fixed to the disturbing potential generated from the GO_CONS_GCF_2_DIR_R5 model while exploiting information from the GRACE and GOCE satellite missions. Precision of the obtained local quasigeoid model is tested by the GNSS/levelling test.

 

[1] Droniou J, Medľa M, Mikula K, Design and analysis of finite volume methods for elliptic equations with oblique derivatives; application to Earth gravity field modelling. Journal of Computational Physics, s. 2019