866 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
Unstructured un-split geometrical Volume-of-Fluid methods -- A review
Geometrical Volume-of-Fluid (VoF) methods mainly support structured meshes,
and only a small number of contributions in the scientific literature report
results with unstructured meshes and three spatial dimensions. Unstructured
meshes are traditionally used for handling geometrically complex solution
domains that are prevalent when simulating problems of industrial relevance.
However, three-dimensional geometrical operations are significantly more
complex than their two-dimensional counterparts, which is confirmed by the
ratio of publications with three-dimensional results on unstructured meshes to
publications with two-dimensional results or support for structured meshes.
Additionally, unstructured meshes present challenges in serial and parallel
computational efficiency, accuracy, implementation complexity, and robustness.
Ongoing research is still very active, focusing on different issues: interface
positioning in general polyhedra, estimation of interface normal vectors,
advection accuracy, and parallel and serial computational efficiency.
This survey tries to give a complete and critical overview of classical, as
well as contemporary geometrical VOF methods with concise explanations of the
underlying ideas and sub-algorithms, focusing primarily on unstructured meshes
and three dimensional calculations. Reviewed methods are listed in historical
order and compared in terms of accuracy and computational efficiency
OpenFOAM Finite Volume Solver for Fluid-Solid Interaction
This paper describes a self-contained parallel fluid-structure interaction solver based on a finite volume discretisation, where a strongly coupled partitioned solution procedure is employed. The incompressible fluid flow is described by the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian form, and the solid deformation is described by the Saint Venant-Kirchhoff hyperelastic model in the total Lagrangian form. Both the fluid and the solid are discretised in space using the second-order accurate cell-centred finite volume method, and temporal discretisation is performed using the second-order accurate implicit scheme. The method, implemented in open-source software OpenFOAM, is parallelised using the domain decomposition approach and the exchange of information at the fluid-solid interface is handled using global face zones. The performance of the solver is evaluated in standard two- and threedimensional cases and excellent agreement with the available numerical results is obtained
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