相关论文: Learning Stable Galerkin Models of Turbulence with…

For the simulation of rectilinearly moving conductors across a magnetic field, the Galer-kin finite element method (GFEM) is generally employed. The inherent instability of GFEM is very often addressed by employing Streamline…

Model-reduction techniques aim to reduce the computational complexity of simulating dynamical systems by applying a (Petrov-)Galerkin projection process that enforces the dynamics to evolve in a low-dimensional subspace of the original…

We propose and analyze a pressure-stabilized projection Lagrange--Galerkin scheme for the transient Oseen problem. The proposed scheme inherits the following advantages from the projection Lagrange--Galerkin scheme. The first advantage is…

We present a numerical methodology for construction of reduced order models, ROMs, of fluid flows through the combination of flow modal decomposition and regression analysis. Spectral proper orthogonal decomposition, SPOD, is applied to…

We propose to accelerate a high order discontinuous Galerkin solver using neural networks. We include a corrective forcing to a low polynomial order simulation to enhance its accuracy. The forcing is obtained by training a deep fully…

This work is devoted to the design of interior penalty discontinuous Galerkin (dG) schemes that preserve maximum principles at the discrete level for the steady transport and convection-diffusion problems and the respective transient…

In uncertainty quantification, critical parameters of mathematical models are substituted by random variables. We consider dynamical systems composed of ordinary differential equations. The unknown solution is expanded into an orthogonal…

This work uses high-order discontinuous Galerkin discretization techniques as a generic, parameter-free, and reliable tool to accurately predict transitional and turbulent flows through medical devices. Flows through medical devices are…

In recent years several research efforts focused on the development of high-order discontinuous Galerkin (dG) methods for scale resolving simulations of turbulent flows. Nevertheless, in the context of incompressible flow computations, the…

Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…

A new high order accurate staggered semi-implicit space-time discontinuous Galerkin (DG) method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space dimensions. The staggered DG…

We propose a technique for performing spectral (in time) analysis of spatially-resolved flowfield data, without needing any temporal resolution or information. This is achieved by combining projection-based reduced-order modeling with…

Grad-div stabilization is a classical remedy in conforming mixed finite element methods for incompressible flow problems, for mitigating velocity errors that are sometimes called poor mass conservation. Such errors arise due to the…

This paper presents an energy-preserving machine learning method for inferring reduced-order models (ROMs) by exploiting the multi-symplectic form of partial differential equations (PDEs). The vast majority of energy-preserving…

We investigate reduced-order models for acoustic and electromagnetic wave problems in parametrically defined domains. The parameter-to-solution maps are approximated following the so-called Galerkin POD-NN method, which combines the…

High-order methods are well-suited for the numerical simulation of complex compressible turbulent flows, but require additional stabilization techniques to capture instabilities arising from the underlying non-linear hyperbolic equations.…

Recently, Gaussian processes have been used to model the vector field of continuous dynamical systems, referred to as GPODEs, which are characterized by a probabilistic ODE equation. Bayesian inference for these models has been extensively…

In this work, we analyze an unfitted discontinuous Galerkin discretization for the numerical solution of the Stokes system based on equal higher-order discontinuous velocities and pressures. This approach combines the best from both worlds,…

We present a quantitative assessment of the impact of high-order mappings on the simulation of flows over complex orography. Curved boundaries were not used in early numerical methods, whereas they are employed to an increasing extent in…

In this work, we propose a Proper Orthogonal Decomposition-Reduced Order Model (POD-ROM) applied to time-splitting schemes for solving the Navier-Stokes equations with open boundary conditions. In this method, we combine three strategies to…