159,787 research outputs found
Arbitrary-Lagrangian-Eulerian discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes
We present a new family of high order accurate fully discrete one-step
Discontinuous Galerkin (DG) finite element schemes on moving unstructured
meshes for the solution of nonlinear hyperbolic PDE in multiple space
dimensions, which may also include parabolic terms in order to model
dissipative transport processes. High order piecewise polynomials are adopted
to represent the discrete solution at each time level and within each spatial
control volume of the computational grid, while high order of accuracy in time
is achieved by the ADER approach. In our algorithm the spatial mesh
configuration can be defined in two different ways: either by an isoparametric
approach that generates curved control volumes, or by a piecewise linear
decomposition of each spatial control volume into simplex sub-elements. Our
numerical method belongs to the category of direct
Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation
formulation of the governing PDE system is considered and which already takes
into account the new grid geometry directly during the computation of the
numerical fluxes. Our new Lagrangian-type DG scheme adopts the novel a
posteriori sub-cell finite volume limiter method, in which the validity of the
candidate solution produced in each cell by an unlimited ADER-DG scheme is
verified against a set of physical and numerical detection criteria. Those
cells which do not satisfy all of the above criteria are flagged as troubled
cells and are recomputed with a second order TVD finite volume scheme. The
numerical convergence rates of the new ALE ADER-DG schemes are studied up to
fourth order in space and time and several test problems are simulated.
Finally, an application inspired by Inertial Confinement Fusion (ICF) type
flows is considered by solving the Euler equations and the PDE of viscous and
resistive magnetohydrodynamics (VRMHD).Comment: 39 pages, 21 figure
Fast Isogeometric Boundary Element Method based on Independent Field Approximation
An isogeometric boundary element method for problems in elasticity is
presented, which is based on an independent approximation for the geometry,
traction and displacement field. This enables a flexible choice of refinement
strategies, permits an efficient evaluation of geometry related information, a
mixed collocation scheme which deals with discontinuous tractions along
non-smooth boundaries and a significant reduction of the right hand side of the
system of equations for common boundary conditions. All these benefits are
achieved without any loss of accuracy compared to conventional isogeometric
formulations. The system matrices are approximated by means of hierarchical
matrices to reduce the computational complexity for large scale analysis. For
the required geometrical bisection of the domain, a strategy for the evaluation
of bounding boxes containing the supports of NURBS basis functions is
presented. The versatility and accuracy of the proposed methodology is
demonstrated by convergence studies showing optimal rates and real world
examples in two and three dimensions.Comment: 32 pages, 27 figure
Multiscale computational first order homogenization of thick shells for the analysis of out-of-plane loaded masonry walls
This work presents a multiscale method based on computational homogenization for the analysis of general heterogeneous thick shell structures, with special focus on periodic brick-masonry walls. The proposed method is designed for the analysis of shells whose micro-structure is heterogeneous in the in-plane directions, but initially homogeneous in the shell-thickness direction, a structural topology that can be found in single-leaf brick masonry walls. Under this assumption, this work proposes an efficient homogenization scheme where both the macro-scale and the micro-scale are described by the same shell theory. The proposed method is then applied to the analysis of out-of-plane loaded brick-masonry walls, and compared to experimental and micro-modeling results.Peer ReviewedPostprint (author's final draft
A level-set method for the evolution of cells and tissue during curvature-controlled growth
Most biological tissues grow by the synthesis of new material close to the
tissue's interface, where spatial interactions can exert strong geometric
influences on the local rate of growth. These geometric influences may be
mechanistic, or cell behavioural in nature. The control of geometry on tissue
growth has been evidenced in many in-vivo and in-vitro experiments, including
bone remodelling, wound healing, and tissue engineering scaffolds. In this
paper, we propose a generalisation of a mathematical model that captures the
mechanistic influence of curvature on the joint evolution of cell density and
tissue shape during tissue growth. This generalisation allows us to simulate
abrupt topological changes such as tissue fragmentation and tissue fusion, as
well as three dimensional cases, through a level-set-based method. The
level-set method developed introduces another Eulerian field than the level-set
function. This additional field represents the surface density of tissue
synthesising cells, anticipated at future locations of the interface. Numerical
tests performed with this level-set-based method show that numerical
conservation of cells is a good indicator of simulation accuracy, particularly
when cusps develop in the tissue's interface. We apply this new model to
several situations of curvature-controlled tissue evolutions that include
fragmentation and fusion.Comment: 15 pages, 10 figures, 3 supplementary figure
- …