Related papers: Efficient probabilistic surrogate modeling techniq…
This paper presents a new numerical method for the compressible Navier-Stokes equations governing the flow of an ideal isentropic gas. To approximate the continuity equation, the method utilizes a discontinuous Galerkin discretization on…
Established techniques for simulation and prediction with Gaussian process (GP) dynamics often implicitly make use of an independence assumption on successive function evaluations of the dynamics model. This can result in significant error…
In this paper, we consider queueing systems where the dynamics are non-stationary and state-dependent. For performance analysis of these systems, fluid and diffusion models have been typically used. Although they are proven to be…
This paper aims to compare and evaluate various obstacle approximation techniques employed in the context of the steady incompressible Navier-Stokes equations. Specifically, we investigate the effectiveness of a standard volume penalization…
While complex simulations of physical systems have been widely used in engineering and scientific computing, lowering their often prohibitive computational requirements has only recently been tackled by deep learning approaches. In this…
This letter presents a non-parametric modeling approach for forecasting stochastic dynamical systems on low-dimensional manifolds. The key idea is to represent the discrete shift maps on a smooth basis which can be obtained by the diffusion…
Resolvent analysis is a powerful tool for modeling and analyzing turbulent flows and in particular provides an approximation of coherent flow structures. Despite recent algorithmic advances, computing resolvent modes for flows with more…
In the present study, the efficiency of preconditioners for solving linear systems associated with the discretized variable-density incompressible Navier-Stokes equations with semiimplicit second-order accuracy in time and spectral accuracy…
Flow-based generative modeling is a powerful tool for solving inverse problems in physical sciences that can be used for sampling and likelihood evaluation with much lower inference times than traditional methods. We propose to refine flows…
Navier-Stokes equations are significant partial differential equations that describe the motion of fluids such as liquids and air. Due to the importance of Navier-Stokes equations, the development on efficient numerical schemes is important…
Nudging is an important data assimilation technique where partial field measurements are used to control the evolution of a dynamical system and/or to reconstruct the entire phase-space configuration of the supplied flow. Here, we apply it…
The Navier--Stokes equations are commonly used to model and to simulate flow phenomena. We introduce the basic equations and discuss the standard methods for the spatial and temporal discretization. We analyse the semi-discrete equations --…
We present a numerical scheme for approximating the incompressible Navier-Stokes equations based on an auxiliary variable associated with the total system energy. By introducing a dynamic equation for the auxiliary variable and…
A probabilistic machine learning model is introduced to augment the $k-\omega\ SST$ turbulence model in order to improve the modelling of separated flows and the generalisability of learnt corrections. Increasingly, machine learning methods…
In chemical process engineering, surrogate models of complex systems are often necessary for tasks of domain exploration, sensitivity analysis of the design parameters, and optimization. A suite of computational fluid dynamics (CFD)…
This paper deals with the derivation of compressible two-phase flow models. We use a thin domain approximation of a two-layer configuration governed by the Navier-Stokes equations, following the works [H. B. Stewart and B. Wendroff, J.…
Exact unstable solutions of the Navier-Stokes equations are thought to underpin the dynamics of turbulence, but are usually computed in minimal computational domains. Here, we extend this dynamical systems approach to spatially extended…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
We propose and analyze unfitted finite element approximations for the two-phase incompressible Navier--Stokes flow in an axisymmetric setting. The discretized schemes are based on an Eulerian weak formulation for the Navier--Stokes equation…
A constructive numerical approximation of the two-dimensional unsteady stochastic Navier-Stokes equations of an incompressible fluid is proposed via a pseudo-compressibility technique involving a parameter $\epsilon$. Space and time are…