A modified Finite Element formulation for the imposition of the slip boundary condition over embedded volumeless geometries

Abstract

Highlights are optional yet highly encouraged for this journal, as they increase the discoverability of your article via search engines. They consist of a short collection of bullet points that capture the novel results of your research as well as new methods that were used during the study (if any). Please have a look at the examples here: example Highlights. Highlights should be submitted in a separate editable file in the online submission system. Please use 'Highlights' in the file name and include 3 to 5 bullet points (maximum 85 characters, including spaces, per bullet point).

Nonconforming Dirichlet boundary conditions in implicit material point method by means of penalty augmentation

“…In MPM, differently from other Lagrangian mesh-based approaches, boundary conditions often need to be applied on boundaries which does not match with the background mesh. Similar problems appears in the unfitted methods for computational fluid dynamics (CFD) problems [24][25][26][27][28].…”

“…Numerical instability could appear when the nonconforming boundary intersects the background mesh very close to one of its edges. This instability is commonly known as the ''small-cut'' instability, very common also in FEM-based unfitted approaches [28,74]. To overcome this issue a simple modification to the shape function values is performed while constructing matrix H in Eq.…”

D7.2 Finalization of "deterministic" verification and validation tests

“…As expected, the computational mesh in the inner block is the same for all embedded simulations, which is the main advantage of the novel embedded CFD method, that is, the simplicity of generating computational meshes for complex geometries. The employed implementation of the embedded approach [14] using the AUSAS discontinuous basis functions [1] expects a tessellation describing the embedded object. Then a robust algorithm for finding the intersection of the skin of the embedded object with the background mesh within KRATOS MultiPhysics is used [2].…”

D6.4 Report on stochastic optimisation for unsteady problems

“…Within this work, the geometry subject to shape optimisation encounters shape updates driven by the gradient-descent optimisation algorithm employed. The embedded CFD approach as proposed in Zorrilla et al 2019 is herein used in the preliminary results. However, for the simulations with a high Reynolds number, a very fine mesh resolution is required for the representation of the building geometry and hence a body-fitted approach with mesh generation is also being explored.…”

“…The corresponding variational formulation of the VMS-stabilised Navier-Stokes equations is extended by Nitsche-type terms accounting for a weakly-zero-velocity field along the boundary of the embedded geometry. The formulation of the momentum conservation includes a penalty term on the embedded boundary to constrain the normal projection of velocity in order to ensure non-penetration (see Zorrilla et al 2019, for details).…”