[1] In light of the increasing number of drifting buoys in the ocean and recent advances in the realism of ocean general circulation models toward oceanic forecasting, the problem of assimilation of Lagrangian observations data in Eulerian models is investigated. A new and general rigorous approach is developed based on optimal interpolation (OI) methods, which takes into account directly the L...

A hybrid approach to the problem of predicting the dispersion of contaminants (e.g. suspended solids or heated water) in coastal areas is presented. A neutral random walk particle tracking method is adopted in the vicinity of the source point, where steep concentration gradients occur. In the case of heat dispersion particles are assigned with buoyancy, which leads to additive horizontal diffus...

We present a method for applying implicit forces on a Lagrangian mesh to an Eulerian discretization of the Navier Stokes equations in a way that produces a sparse symmetric positive definite system. The resulting method has implicit and fully coupled viscosity, pressure, and Lagrangian forces. We apply our new framework for forces on a Lagrangian mesh to the case of surface tension force, which...

In this study, we establish a hybrid high-order smoothed particle hydrodynamics (SPH) framework (MLS-TENO-SPH) for compressible flows with discontinuities, which is able to achieve genuine convergence in smooth regions and also capture discontinuities well non-smooth regions. The can be either fully Lagrangian, Eulerian or realizing arbitary-Lagrangian-Eulerian (ALE) feature enforcing the isotr...

This contribution is the first part of two papers on the Fully Eulerian formulation for fluid-structure interactions. We derive a monolithic variational formulation for the coupled problem in Eulerian coordinates. Further, we present the Initial Point Set method for capturing the moving interface. For the discretization of this interface problem, we introduce a modified finite element scheme th...

The paper presents a theory for modeling flow in anisotropic, viscous rock. This theory has originally been developed for the simulation of large deformation processes including the folding and kinking of multi-layered visco-elastic rock (Mühlhaus et al. [1],[2]). The orientation of slip planes in the context of crystallographic slip is determined by the normal vector — the director — of these ...