Related papers: Bayesian-Enhanced Galerkin-Based Reduced Order Mod…
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…
In this paper we present a novel approach for the design of high order general boundary conditions when approximating solutions of the Euler equations on domains with curved boundaries, using meshes which may not be boundary conformal. When…
Modeling real-world multidimensional time series can be particularly challenging when these are sporadically observed (i.e., sampling is irregular both in time and across dimensions)-such as in the case of clinical patient data. To address…
We present a reduced order method (ROM) based on proper orthogonal decomposition (POD) for the viscous Burgers' equation and the incompressible Navier-Stokes equations discretized using an implicit-explicit hybrid discontinuous…
The purpose of this work is to present a reduced order modeling framework for parametrized turbulent flows with moderately high Reynolds numbers within the variational multiscale (VMS) method. The Reduced Order Models (ROMs) presented in…
Computational fluid dynamics (CFD) simulations play an important role in engineering science and applications, however, it is not applicable for problems requiring a large number of repeated calculations. Accordingly, many reduced-order…
We investigate a numerical behaviour of robust deterministic optimal control problem subject to a convection diffusion equation containing uncertain inputs. Stochastic Galerkin approach, turning the original optimization problem containing…
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…
This paper deals with the numerical modeling of flow around and through a porous obstacle by a reduced order model (ROM) obtained by Galerkin projection of the Navier-Stokes equations onto a Proper Orthogonal Decomposition (POD) reduced…
We investigate a hierarchy of eddy-viscosity terms in POD Galerkin models to account for a large fraction of unresolved fluctuation energy. These Galerkin methods are applied to Large Eddy Simulation data for a flow around the vehicle-like…
Ordinary differential equation (ODE) models are widely used to describe systems in many areas of science. To ensure these models provide accurate and interpretable representations of real-world dynamics, it is often necessary to infer…
The objective of this paper is to investigate how noisy and incomplete observations can be integrated in the process of building a reduced-order model. This problematic arises in many scientific domains where there exists a need for…
This paper proposes a supervised machine learning framework for the non-intrusive model order reduction of unsteady fluid flows to provide accurate predictions of non-stationary state variables when the control parameter values vary. Our…
We present a high-order implicit large-eddy simulation (ILES) approach for simulating transitional turbulent flows. The approach consists of an Interior Embedded Discontinuous Galerkin (IEDG) method for the discretization of the…
We develop a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for the efficient numerical simulation of the parametric Navier-Stokes equations in the stream function-vorticity formulation. Unlike previous…
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.…
This research paper investigates the Adjoint Petrov-Galerkin (APG) method for reduced order models (ROM) and fluid dynamics governed by the incompressible Navier-Stokes equations. The Adjoint Petrov-Galerkin ROM, derived using the…
An hyperelastic biphasic model is presented. For slow-draining problems (permeability less than 1\times10-2 mm4 N-1 s-1), numerical instabilities in the form of non-physical oscillations in the pressure field are observed in 3D problems…
Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…
Generally, reduced order models of fluid flows are obtained by projecting the Navier-Stokes equations onto a reduced subspace spanned by vector functions that carry the meaningful information of the dynamics. A common method to generate…