Search results for "Discontinuous Galerkin"
showing 10 items of 27 documents
Adaptive discontinuous evolution Galerkin method for dry atmospheric flow
2014
We present a new adaptive genuinely multidimensional method within the framework of the discontinuous Galerkin method. The discontinuous evolution Galerkin (DEG) method couples a discontinuous Galerkin formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems, such that all of the infinitely many directions of wave propagation are considered explicitly. In order to take into account multiscale phenomena that typically appear in atmospheric flows nonlinear fluxes are split into a linear part governing the acoustic and gravitational waves and a nonlinear part that models advection. Time integration is realiz…
Discontinuous Galerkin models for composite multilayered shells with higher order kinematics
2021
Composite multilayered shells are widely employed in aerospace, automotive and civil engineering as weight-saving structural components. In multilayered shells, despite its versatility, the interplay between the curved geometry and the properties of the composite layers induces a complex distribution of the mechanical fields, which must be accurately resolved to safely employ generally curved composite shells as load-bearing structures. The problem can be addressed through the two-dimensional shell theories, which are based on suitable assumptions on the behavior of the mechanical fields throughout the thickness of the considered structures and are a viable strategy for reducing the computa…
Parallel finite element splitting-up method for parabolic problems
1991
An efficient method for solving parabolic systems is presented. The proposed method is based on the splitting-up principle in which the problem is reduced to a series of independent 1D problems. This enables it to be used with parallel processors. We can solve multidimensional problems by applying only the 1D method and consequently avoid the difficulties in constructing a finite element space for multidimensional problems. The method is suitable for general domains as well as rectangular domains. Every 1D subproblem is solved by applying cubic B-splines. Several numerical examples are presented.
Molecular dynamics simulations in hybrid particle-continuum schemes: Pitfalls and caveats
2017
Heterogeneous multiscale methods (HMM) combine molecular accuracy of particle-based simulations with the computational efficiency of continuum descriptions to model flow in soft matter liquids. In these schemes, molecular simulations typically pose a computational bottleneck, which we investigate in detail in this study. We find that it is preferable to simulate many small systems as opposed to a few large systems, and that a choice of a simple isokinetic thermostat is typically sufficient while thermostats such as Lowe-Andersen allow for simulations at elevated viscosity. We discuss suitable choices for time steps and finite-size effects which arise in the limit of very small simulation bo…
Approximate Lax–Wendroff discontinuous Galerkin methods for hyperbolic conservation laws
2017
Abstract The Lax–Wendroff time discretization is an alternative method to the popular total variation diminishing Runge–Kutta time discretization of discontinuous Galerkin schemes for the numerical solution of hyperbolic conservation laws. The resulting fully discrete schemes are known as LWDG and RKDG methods, respectively. Although LWDG methods are in general more compact and efficient than RKDG methods of comparable order of accuracy, the formulation of LWDG methods involves the successive computation of exact flux derivatives. This procedure allows one to construct schemes of arbitrary formal order of accuracy in space and time. A new approximation procedure avoids the computation of ex…
HIGH-ORDER ACCURATE EMBEDDED-BOUNDARY DISCONTINUOUS GALERKIN METHODS FOR INVISCID GAS DYNAMICS
2022
This work presents a computational framework for solving the equations of inviscid gas dynamics over embedded geometries based on the discontinuous Galerkin (DG) method. The novelty of the framework is the ability to achieve high-order accuracy in the regions of smooth flow and to handle the presence of solution discontinuities via suitably introduced damping terms, which allow controlling spurious oscillations that are typical of high-order methods for first-order hyperbolic PDEs. The framework employs block structured Cartesian grids where a level set function defines implicitly the considered geometry. The domain is partitioned by intersecting the grid and the level set function, such th…
Finite deformation analysis of laminated shell via the discontinuous Galerkin method
2022
In this work, we propose a novel formulation for the large displacements and post-buckling response analysis of laminated composite shell structures. In order to accurately recover the solution in the case of multilayered shells, the covariant components of the displacement field are approximated through the thickness using high-order structural theories. The non-linear two-dimensional total Lagrangian formulation is obtained starting from the Principle of Virtual Displacements for the three-dimensional elasticity assuming a linear constitutive relationship between the second Piola–Kirchhoff stress tensor and the Green-Lagrange strain tensor. The discontinuous Galerkin method is used in com…
IMPLICIT MESH DISCONTINUOUS GALERKIN FOR VARIABLE ANGLE TOW MULTILAYERED PLATES
2018
This works presents a novel computational scheme for variable angle tow (VAT) multilayered plates [1]. The characteristic features of the proposed scheme are the combined use of a discontinuous Galerkin (dG) formulation and an implicitly defined mesh. The formulation is based on the principle of virtual displacements (PVD) and the Equivalent Single Layer (ESL) assumption for the mechanical behavior of the VAT plates [2]. The problem is first placed within the dG framework by suitably introducing an auxiliary variable and by rewriting the set of equations governing ESL VAT plates as a firstorder system of differential equations. Following Arnold et al.[3] and by introducing suitably defined …
TRANSIENT AND FREE-VIBRATION ANALYSIS OF LAMINATED SHELLS THROUGH THE DISCONTINUOUS GALERKIN METHOD
2022
This paper presents a novel formulation for linear transient and free-vibration analysis of laminated shell structures based on Interior Penalty discontinuous Galerkin (DG) methods and variable-order through-the-thickness kinematics, whose combined use allows solving the shell problem with high-order accuracy throughout both the shell thickness and the shell modelling domain. The shell geometry is described via a generic system of curvilinear coordinates using either an analytical or a NURBS-based parametrization of the shell mid surface; the formulation also allows for the presence of cut-outs, which are implicitly represented by means of a level set function. After deriving the governing …
Buckling analysis of multilayered structures using high-order theories and the implicit-mesh discontinuous Galerkin method
2022
This work presents a novel formulation for the linear buckling analysis of multilayered shells. The formulation employs high-order Equivalent-Single-Layer (ESL) shell theories based on the through-the-thickness expansion of the covariant components of the displacement field, whilst the corresponding buckling problem is derived using the Euler’s method. The novelty of the formulation regards the solution of the governing equations, which is obtained via implicit-mesh discontinuous Galerkin (DG) schemes. The DG method is a high-order accurate numerical technique based on a discontinuous representation of the solution among the mesh elements and on the use of suitably defined boundary integral…