On a depth-averaged numerical simulation of flow phenomena in sedimentary basins
Ney Augusto Dumont1; Elvis Yuri Mamani1; Carlos Andrés Aguilar1; Hélvio de Farias Costa Peixoto1; Alexandre Antonio de Oliveira Lopes2; Stefane Lopes2
1 Pontifical Catholic University of Rio de Janeiro; 2 Petrosoft Design
doi:10.20906/CPS/CILAMCE2015-0839
Resumo
The ultimate goal of the present developments is the depth-averaged simulation of three-dimensional transport phenomena in sedimentary basins. The continuity and momentum equations that govern the problem are by nature highly non-linear, domain-driven and time-dependent. However, it has become possible to reduce the depth-averaged equations to a stream function-vorticity model plus a complementary equation. A variationally hybrid boundary element formulation (HBEM) is resorted to for the iterative solution of a problem in an arbitrarily shaped, irregular domain embedded in a regular finite-difference (FD) grid. In each iteration, the non-linear terms are taken into account from the previous results in the frame of a FD scheme, as an arbitrary particular solution for which the boundary conditions are of no relevancy. This estimate solution is then added to the homogeneous part of the differential equations, which have been numerically discretized in terms of the HBEM. Improved HBEM results are obtained after considering the boundary conditions of the problem as a whole. Uncontrollable round-off errors may occur if the FD particular solution related to the domain, non-linear terms is too far apart from the sought solution. A relaxation factor may be required to guarantee stability of the iterative process and convergence of results. Besides the formulation, the paper also presents a few numerical examples to validate the proposed model as well as to assess its performance in terms of convergence of results.
Palavras-chave: Hybrid boundary elements; Navier Stokes equations; non-linear equations; irregular domains; embedded formulation