Parallel adaptive simulation of gravity currents on the lock-exchange problem

A good representation of the displacement front and the interface between different density fluids are essential in gravity currents simulations. Adaptive meshes play a key issue to ensure the solution quality performing the automatic refinement locally in regions where it is necessary, leaving most of the domain coarsely discretized. In this work, a stabilized FEM is applied to modelling three-dimensional gravity currents phenomena. Parallel AMR/C, provided by the libMesh FEM open source library, is performed, and the results obtained by different adaptivity configurations are compared with those from fixed meshes. An a posteriori error estimator for the mesh AMR/C procedure based on scalar flux jumps between adjacent elements is adopted. Mesh adaptivity proves to be a very effective approach in reducing the total number of elements and at the same time to be able to successfully capture the main characteristics of the flow dynamics, as the development of Kelvin-Helmholtz billows and the formation of lobes and clefts.