In previous work, we introduced a space-time embedded-hybridizable discontinuous Galerkin method for the solution of incompressible Navier–Stokes equations on time-dependent domains which motion domain is prescribed. This discretization exactly mass conserving, locally momentum and energy-stable. this article, extend to fluid-rigid body interaction problems in fluid not known priori. To account...

The development of adaptive mesh refinement capabilities in the field of computational fluid dynamics is an essential tool for enabling the simulation of larger and more complex physical problems. In this report, we describe recent developments that have been made to enable adaptive mesh refinement in Nek5000 and we validate the method on simple, two–dimensional, steady test cases. We start by ...

Generation of manifold mesh is an urgent issue in mathematical simulations of biomolecule using boundary element methods (BEM) or finite element method (FEM). Defects, such as not closed mesh, intersection of elements and missing of small structures, exist in surface meshes generated by most of the current meshing method. Usually the molecular surface meshes produced by existing methods need to...

In this paper we present a new framework for multilevel preconditioning of large sparse systems of linear algebraic equations arising from the interior penalty discontinuous Galerkin approximation of second-order elliptic boundary value problems. Though the focus is on a particular family of rotated bilinear non-conforming (Rannacher-Turek) finite elements in two space dimensions (2D) the propo...

A co-volume scheme is introduced for the rotating shallow water equations, in which both velocity components are specified on cell edges, and the thickness variables evolve on both the primary and the dual cell centers. The scheme applies to generic, conforming and non-orthogonal staggered grids, including the widely used lat-lon quadrilateral grids and the Delaunay-Voronoi tessellations. It ca...

A novel node-based smoothing element for triangular and quadrilateral meshes is presented for static analysis of planar piezoelectric structures. In contrast to the smoothed finite element formulation that was based on sub-cells within an original quadrilateral element, this new method transforms a general original finite element mesh into a mesh of new smoothing cells individually associated w...

Reaction-diffusion equations can present solutions in the form of traveling waves with stiff wave fronts. Such evolve different spatial and temporal scales, it is desired to construct numerical methods that adopt refinement at locations where solution becomes stiff. In this work, we develop a high-order adaptive mesh method based on Chebyshev spectral multidomain approach for reaction-diffusion...

We study the two dimensional time dependent Large Eddy Simulation method applied to incompressible Navier–Stokes system with Smagorinsky’s eddy viscosity model and a filter width that depends on local mesh size. The discrete is based implicit Euler scheme conforming finite element for space discretizations, respectively. establish reliable efficient posteriori error estimation between numerical...

Longest edge refinement algorithms were designed to deal with the iterative and local refinement of triangulations for finite element applications. In 3-dimensions the algorithm locally refines a tetredra set Sref and some neighboring tetraedra in each iteration. The new points introduced in the mesh are midpoints of the longest edge of some tetrahedra of either of the input mesh or of some ref...

A B-conforming time-stepping Volume Integral Method (VIM) formulation for nonlinear 3D field-circuit coupled problems is presented in this paper. The advantage of the VIM with respect to Finite Element (FEM) that only ferromagnetic regions have be discretized, thus avoiding mesh air. It an appealing approach given it avoids numerical errors can arise from meshing direct explained, assembling a ...