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Related papers: On long-term boundedness of Galerkin models

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We propose an aerodynamic force model associated with a Galerkin model for the unforced fluidic pinball, the two-dimensional flow around three equal cylinders with one radius distance to each other. The starting point is a Galerkin model of…

Fluid Dynamics · Physics 2021-05-19 Nan Deng , Bernd R. Noack , Marek Morzyński , Luc R. Pastur

In this work we construct reliable a posteriori estimates for some discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appropriate reconstructions of the discrete solution together…

Numerical Analysis · Mathematics 2023-03-01 Jan Giesselmann , Charalambos Makridakis , Tristan Pryer

Stochastic Galerkin formulations of the two-dimensional shallow water systems parameterized with random variables may lose hyperbolicity, and hence change the nature of the original model. In this work, we present a hyperbolicity-preserving…

Numerical Analysis · Mathematics 2022-01-26 Dihan Dai , Yekaterina Epshteyn , Akil Narayan

In this paper, we develop a new mass conservative numerical scheme for the simulations of a class of fluid-structure interaction problems. We will use the immersed boundary method to model the fluid-structure interaction, while the fluid…

Numerical Analysis · Mathematics 2018-06-21 Siu Wun Cheung , Eric Chung , Hyea Hyun Kim

For finite element approximations of transport phenomena, it is often necessary to apply a form of limiting to ensure that the discrete solution remains well-behaved and satisfies physical constraints. However, these limiting procedures are…

Numerical Analysis · Mathematics 2024-04-12 Tarik Dzanic

We present and analyze a discontinuous Galerkin method for the numerical modeling of the non-linear fully-coupled thermo-hydro-mechanic problem. We propose a high-order symmetric weighted interior penalty scheme that supports general…

Numerical Analysis · Mathematics 2023-11-28 Stefano Bonetti , Michele Botti , Paola F. Antonietti

We consider the problem of determining the class of continuous-time dynamical systems that can be globally linearized in the sense of admitting an embedding into a linear system on a higher-dimensional Euclidean space. We solve this problem…

Dynamical Systems · Mathematics 2026-04-08 Matthew D. Kvalheim , Philip Arathoon

Non-autonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but…

Chaotic Dynamics · Physics 2020-09-24 Julia Cantisán , Jesús M. Seoane , Miguel A. F. Sanjuán

A fully discrete Galerkin scheme for a thermodynamically consistent transient Max-well-Stefan system for the mass particle densities, coupled to the Poisson equation for the electric potential, is investigated. The system models the…

Numerical Analysis · Mathematics 2018-09-05 Ansgar Jüngel , Oliver Leingang

We consider the numerical approximation of compressible flow in a pipe network. Appropriate coupling conditions are formulated that allow us to derive a variational characterization of solutions and to prove global balance laws for the…

Numerical Analysis · Mathematics 2016-10-06 Herbert Egger

Plasmas are highly nonlinear and multi-scale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD). Galerkin models,…

Plasma Physics · Physics 2021-01-12 Alan A. Kaptanoglu , Kyle D. Morgan , Christopher J. Hansen , Steven L. Brunton

We formulate a coupled surface/subsurface flow model that relies on hydrostatic equations with free surface in the free flow domain and on the Darcy model in the subsurface part. The model is discretized using the local discontinuous…

Numerical Analysis · Mathematics 2018-06-12 Andreas Rupp , Vadym Aizinger , Balthasar Reuter , Peter Knabner

Our aim is to analyse special type of boundary conditions, created to simulate flows like in cardiovascular and respiratory systems. Firstly, we will describe model of viscous, incompressible fluid in a domain consisting many inlets and…

Analysis of PDEs · Mathematics 2020-02-11 Kamil Wołos , Przemysław Kosewski

The development and application of the Discontinuous Galerkin (DG) method have attracted great attention in computational fluid dynamics (CFD) com- munity in the past decades. The underlying reason for such an intensive investigation is due…

Numerical Analysis · Mathematics 2016-01-20 Kun Xu , Chang Liu , Xiaodong Ren

The shallow water flow model is widely used to describe water flows in rivers, lakes, and coastal areas. Accounting for uncertainty in the corresponding transport-dominated nonlinear PDE models presents theoretical and numerical challenges…

Numerical Analysis · Mathematics 2023-10-11 Dihan Dai , Yekaterina Epshteyn , Akil Narayan

We propose and rigorously analyse semi- and fully discrete discontinuous Galerkin methods for an initial and boundary value problem describing inertial viscoelasticity in terms of elastic and viscoelastic stress components, and with mixed…

Numerical Analysis · Mathematics 2023-06-27 Salim Meddahi , Ricardo Ruiz-Baier

Discontinuous Galerkin methods are developed for solving the Vlasov-Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy. Such properties in…

Numerical Analysis · Mathematics 2013-10-24 Yingda Cheng , Irene M. Gamba , Fengyan Li , Philip J. Morrison

A novel wetting and drying treatment for second-order Runge-Kutta discontinuous Galerkin (RKDG2) methods solving the non-linear shallow water equations is proposed. It is developed for general conforming two-dimensional triangular meshes…

Numerical Analysis · Mathematics 2019-08-08 Stefan Vater , Nicole Beisiegel , Jörn Behrens

We give an a posteriori analysis of a semi-discrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics, which involves an energy density depending not only on the strain but also the strain…

Numerical Analysis · Mathematics 2023-03-01 Jan Giesselmann , Tristan Pryer

An efficient time-stepping algorithm is proposed based on operator-splitting and the space-time discontinuous Galerkin finite element method for problems in the non-classical theory of thermoelasticity. The non-classical theory incorporates…

Numerical Analysis · Mathematics 2015-05-05 Mebratu F. Wakeni , B. D. Reddy , A. T. McBride