1,720,968 research outputs found
Mass Preserving Finite Element Implementations of Level Set Method
No full textIn the last two decades, the level set method has been extensively used for the numerical solution of interface problems in different domains. The basic idea is to embed the interface as the level set of a regular function. In this paper we focus on the numerical solution of interface advection equations appearing in free-surface fluid dynamics problems, where naive finite element implementations are unsatisfactory. As a matter of fact, practitioners in fluid dynamics often complain that the mass of each fluid component is not conserved, a phenomenon which is therefore often referred to as mass loss. In this paper we propose and compare two finite element implementations that cure this ill-behaviour without the need to resort to combined strategies (such as e.g. particle level set). The first relies on a discontinuous Galerkin discretization, which is known to give very good performance when facing hyperbolic problems; the second is a stabilized continuous FEM implementation based on the stabilization method presented in [16], which is free from many of the problems that classical methods exhibit when applied to unsteady problems
A Hybrid High-Order Discretization Method for Nonlinear Poroelasticity
Full text linkIn this work, we construct and analyze a nonconforming high-order discretization method for the quasi-static single-phase nonlinear poroelasticity problem describing Darcean flow in a deformable porous medium saturated by a slightly compressible fluid. The nonlinear elasticity operator is discretized using a Hybrid High-Order method, while the Darcy operator relies on a Symmetric Weighted Interior Penalty discontinuous Galerkin scheme. The method is valid in two and three space dimensions, delivers an inf-sup stable discretization on general meshes including polyhedral elements and nonmatching interfaces, supports arbitrary approximation orders, and has a reduced cost thanks to the possibility of statically condensing a large subset of the unknowns for linearized versions of the problem. Moreover, the proposed construction can handle both nonzero and vanishing specific storage coefficients
High-order discontinuous Galerkin solution of low- and high-Reynolds number compressible flows
No full textImplementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming
No full textDiscontinuous Skeletal methods approximate the solution of boundary-value problems by attaching discrete unknowns to mesh faces (hence the term skeletal) while allowing these discrete unknowns to be chosen independently on each mesh face (hence the term discontinuous). Cell-based unknowns, which can be eliminated locally by a Schur complement technique (also known as static condensation), are also used in the formulation. Salient examples of high-order Discontinuous Skeletal methods are Hybridizable Discontinuous Galerkin methods and the recently-devised Hybrid High-Order methods. Some major benefits of Discontinuous Skeletal methods are that their construction is dimension-independent and that they offer the possibility to use general meshes with polytopal cells and non-matching interfaces. In this work, we show how this mathematical flexibility can be efficiently replicated in a numerical software using generic programming. We describe a number of generic algorithms and data structures for high-order Discontinuous Skeletal methods within a “write once, run on any kind of mesh” framework. The computational efficiency of the implementation is assessed on the Poisson model problem discretized using various polytopal meshes and the Hybrid High-Order method
An abstract analysis framework for monolithic discretisations of poroelasticity with application to Hybrid High-Order methods
Full text linkIn this work, we introduce a novel abstract framework for the stability and convergence analysis of fully coupled discretisations of the poroelasticity problem and apply it to the analysis of Hybrid High-Order (HHO) schemes. A relevant feature of the proposed framework is that it rests on mild time regularity assumptions that can be derived from an appropriate weak formulation of the continuous problem. To the best of our knowledge, these regularity results for the Biot problem are new. A novel family of HHO discretisation schemes is also proposed and analysed, and their performance numerically evaluated
An implicit high-order discontinuous Galerkin method for steady and unsteady incompressible flows
No full textA Hybrid High-Order Method for Multiple-Network Poroelasticity
Full text linkWe develop Hybrid High-Order methods for multiple-network poroelasticity, modelling seepage through deformable fissured porous media. The proposed methods are designed to support general polygonal and polyhedral elements. This is a crucial feature in geological modelling, where the need for general elements arises, e.g., due to the presence of fracture and faults, to the onset of degenerate elements to account for compaction or erosion, or when nonconforming mesh adaptation is performed. We use as a starting point a mixed weak formulation where an additional total pressure variable is added, that ensures the fulfilment of a discrete inf-sup condition. A complete theoretical analysis is performed, and the results are demonstrated on a panel of numerical tests
Analytical and numerical modeling of microchannel heat sink
No full textAnalytical and numerical tools for modeling microchannel heat sinks are presented, including the most important project parameters. An analytical 1D model, suitable for both design and performance calculations, is first developed under lumped capacitance assumption and resorting to standard correlations for Nu under HI boundary conditions. 2D model extensions are then provided separately for poorly and highly conductive substrates: in the former case axial conduction is neglected; in the latter case the 2D model is modified to include axial conduction by exploiting the results from ID model. This innovative approach provides a significant reduction in computational costs with respect to a conventional 3D model. A 3D model is then developed to evaluate the effects of thermal entrance. Finally, some optimization calculations are performed.</p
An artificial compressibility numerical flux for the discontinuous Galerkin numerical solution of the incompressible Navier-Stokes equations
No full textDiscontinuous Galerkin (DG) methods have proved to be well suited for the construction of robust high-order numerical schemes on unstructured and possibly nonconforming grids for a variety of problems. Their application to the incompressible Navier–Stokes (INS) equations has also been recently considered, although the subject is far from being fully explored. In this work, we propose a new approach for the DG numerical solution of the INS equations written in conservation form. The inviscid numerical fluxes both in the continuity and in the momentum equation are computed using the values of velocity and pressure provided by the (exact) solution of the Riemann problem associated with a local artificial compressibility perturbation of the equations. Unlike in most of the existing methods, artificial compressibility is here introduced only at the interface flux level, therefore resulting in a consistent discretization of the INS equations irrespectively of the amount of artificial compressibility introduced. The discretization of the viscous term follows the well-established DG scheme named BR2. The performance and the accuracy of the method are demonstrated by computing the Kovasznay flow and the two-dimensional lid-driven cavity flow for a wide range of Reynolds numbers and for various degrees of polynomial approximation
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