403 research outputs found
Algorithmic Monotone Multiscale Finite Volume Methods for Porous Media Flow
Multiscale finite volume methods are known to produce reduced systems with
multipoint stencils which, in turn, could give non-monotone and out-of-bound
solutions. We propose a novel solution to the monotonicity issue of multiscale
methods. The proposed algorithmic monotone (AM- MsFV/MsRSB) framework is based
on an algebraic modification to the original MsFV/MsRSB coarse-scale stencil.
The AM-MsFV/MsRSB guarantees monotonic and within bound solutions without
compromising accuracy for various coarsening ratios; hence, it effectively
addresses the challenge of multiscale methods' sensitivity to coarse grid
partitioning choices. Moreover, by preserving the near null space of the
original operator, the AM-MsRSB showed promising performance when integrated in
iterative formulations using both the control volume and the Galerkin-type
restriction operators. We also propose a new approach to enhance the
performance of MsRSB for MPFA discretized systems, particularly targeting the
construction of the prolongation operator. Results show the potential of our
approach in terms of accuracy of the computed basis functions and the overall
convergence behavior of the multiscale solver while ensuring a monotone
solution at all times.Comment: 29 pages, 20 figure
SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES
Crack propagation in thin shell structures due to cutting is conveniently simulated
using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell
elements are usually preferred for the discretization in the presence of complex material
behavior and degradation phenomena such as delamination, since they allow for a correct
representation of the thickness geometry. However, in solid-shell elements the small thickness
leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new
selective mass scaling technique is proposed to increase the time-step size without affecting
accuracy. New ”directional” cohesive interface elements are used in conjunction with selective
mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile
shells
- …