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Related papers: Stochastic Galerkin method for cloud simulation

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Reduced-order models were derived for plane Couette flow using Galerkin projection, with orthonormal basis functions taken as the leading controllability modes of the linearised Navier-Stokes system for a few low wavenumbers. Resulting…

Fluid Dynamics · Physics 2022-07-15 André V. G. Cavalieri , Petrônio A. S. Nogueira

We introduce an immersed high-order discontinuous Galerkin method for solving the compressible Navier-Stokes equations on non-boundary-fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are…

Numerical Analysis · Mathematics 2020-01-08 Hong Xiao , Eky Febrianto , Qiaoling Zhang , Fehmi Cirak

The present works is focused on studying bifurcating solutions in compressible fluid dynamics. On one side, the physics of the problem is thoroughly investigated using high-fidelity simulations of the compressible Navier-Stokes equations…

Numerical Analysis · Mathematics 2022-12-21 Niccolò Tonicello , Andrea Lario , Gianluigi Rozza , Gianmarco Mengaldo

An important class of spatio-temporal models is constructed by leveraging the hierarchical structure of dynamical (or, state-space) models. This paper proposes a new statistical dynamical model for spatio-temporal processes motivated by…

Methodology · Statistics 2026-05-11 Yutong Zhang , Xiao Liu

We investigate the convergence of the Galerkin approximation for the stochastic Navier-Stokes equations in an open bounded domain $\mathcal{O}$ with the non-slip boundary condition. We prove that \begin{equation*} \mathbb{E} \left[ \sup_{t…

Analysis of PDEs · Mathematics 2018-06-06 Igor Kukavica , Kerem Ugurlu , Mohammed Ziane

In this paper a new high order semi-implicit discontinuous Galerkin method (SI-DG) is presented for the solution of the incompressible Navier-Stokes equations on staggered space-time adaptive Cartesian grids (AMR) in two and three…

Numerical Analysis · Mathematics 2017-08-02 Francesco Fambri , Michael Dumbser

The developments over the last five decades concerning numerical discretisations of the incompressible Navier--Stokes equations have lead to reliable tools for their approximation: those include stable methods to properly address the…

Numerical Analysis · Mathematics 2025-08-12 Dominic Breit , Andreas Prohl , Jörn Wichmann

We investigate the propagation of uncertainties in the Aw-Rascle-Zhang model, which belongs to a class of second order traffic flow models described by a system of nonlinear hyperbolic equations. The stochastic quantities are expanded in…

Numerical Analysis · Mathematics 2021-05-06 Stephan Gerster , Michael Herty , Elisa Iacomini

The description of a stellar system as a continuous fluid represents a convenient first approximation to stellar dynamics, and its derivation from the kinetic theory is standard. The challenge lies in providing adequate closure…

Astrophysics · Physics 2007-05-23 Edward A. Spiegel , Jean-Luc Thiffeault

In this paper, we design and analyze staggered discontinuous Galerkin methods of arbitrary polynomial orders for the stationary Navier-Stokes equations on polygonal meshes. The exact divergence-free condition for the velocity is satisfied…

Numerical Analysis · Mathematics 2021-07-21 Dohyun Kim , Lina Zhao , Eric Chung , Eun-Jae Park

We introduce a hybridizable discontinuous Galerkin method for the incompressible Navier--Stokes equations for which the approximate velocity field is pointwise divergence-free. The method builds on the method presented by Labeur and Wells…

Numerical Analysis · Mathematics 2023-07-04 Sander Rhebergen , Garth N. Wells

We present a high-order discontinuous Galerkin (DG) solver of the compressible Navier-Stokes equations for cloud formation processes. The scheme exploits an underlying parallelized implementation of the ADER-DG method with dynamic adaptive…

Computational Physics · Physics 2020-05-18 Lukas Krenz , Leonhard Rannabauer , Michael Bader

This work proposes a method for model reduction of finite-volume models that guarantees the resulting reduced-order model is conservative, thereby preserving the structure intrinsic to finite-volume discretizations. The proposed…

Numerical Analysis · Computer Science 2018-07-04 Kevin Carlberg , Youngsoo Choi , Syuzanna Sargsyan

We explore the unsupervised clustering technique introduced in [25] to identify viscous/turbulent from inviscid regions in incompressible flows. The separation of regions allows solving the Navier-Stokes equations including Large Eddy…

Fluid Dynamics · Physics 2024-03-11 Kheir-Eddine Otmani , Andrés Mateo-Gabín , Gonzalo Rubio , Esteban Ferrer

The paper deals with a stochastic Galerkin approximation of elliptic Dirichlet boundary control problems with random input data. The expectation of a tracking cost functional with the deterministic constrained control is minimized. Error…

Optimization and Control · Mathematics 2025-06-16 Max Winkler , Hamdullah Yücel

A hybrid method for the incompressible Navier--Stokes equations is presented. The method inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order…

Computational Engineering, Finance, and Science · Computer Science 2012-11-19 Robert Jan Labeur , Garth N. Wells

We develop generalized polynomial chaos (gPC) based stochastic Galerkin (SG) methods for a class of highly oscillatory transport equations that arise in semiclassical modeling of non-adiabatic quantum dynamics. These models contain…

Numerical Analysis · Mathematics 2017-04-05 Nicolas Crouseilles , Shi Jin , Mohammed Lemou , Liu Liu

We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration…

Numerical Analysis · Mathematics 2017-08-15 Benjamin Krank , Niklas Fehn , Wolfgang A. Wall , Martin Kronbichler

This work introduces a general framework for establishing the long time accuracy for approximations of Markovian dynamical systems on separable Banach spaces. Our results illuminate the role that a certain uniformity in Wasserstein…

Numerical Analysis · Mathematics 2023-02-06 Nathan E. Glatt-Holtz , Cecilia F. Mondaini

The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product polynomial expansions with respect to the parametric…

Numerical Analysis · Mathematics 2025-03-28 Markus Bachmayr , Martin Eigel , Henrik Eisenmann , Igor Voulis