A shallow water event-driven approach to simulate turbidity currents at stratigraphic scale

Abstract

We present a new event-driven approach that combines a shallow water flow model with a practical sedimentation technique to simulate the formation of turbidite depositional systems at a stratigraphic scale. Equations that govern turbidity currents dynamics are solved using a new finite element flux-corrected transport scheme. In this sense, the low-order formulation is built by adding a novel Rusanovlike scalar dissipation scaled by a shock-capturing operator to standard Galerkin equations. From it, the high-order system is obtained by including anti-diffusive fluxes linearized around the low-order solution and limited with the Zalesak’s algorithm, following a minmod prelimiter. Implicit time integration with adaptive time steps is performed with an iterative nonlinear scheme that linearizes source terms. Sedimentation is implemented by carrying five granulometric fractions (clay, silt, and fine, medium and coarse sands) along evolved streaklines and radially scattering sediments that deposit filling the available space and compacting the underneath sediment layers. The flow is computed while an event discharge into an area of interest is active, or the inflow current has not reached an equilibrium state. Afterward, the event deposition step is executed. Numerical results of our flow solver presented a good agreement with available exact and literature solutions. It is also compared with a stabilized finite element formulation, producing better outcomes, especially in scenarios with complex drying/wetting dynamics. Also, the simulated sediment deposits suggest that our approach is well suited for stratigraphic scale simulations.