Related papers: Ensemble algorithm for parametrized flow problems …
We consider settings for which one needs to perform multiple flow simulations based on the Navier-Stokes equations, each having different values for the physical parameters and/or different initial condition data, boundary conditions data,…
Ensemble calculations are essential for systems with uncertain data but require substantial increase in computational resources. This increase severely limits ensemble size. To reach beyond current limits, we present a first-order…
Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical algorithm is developed to efficiently determine a set of such simulations in which the…
We propose inflow and outflow boundary conditions for the compressible Navier-Stokes equations and prove that they allow a priori estimates of the entropy, mass and total energy. Furthermore, we demonstrate how to approximate these boundary…
In many applications, uncertainty in problem data leads to the need for numerous computationally expensive simulations. This report addresses this challenge by developing a penalty-based ensemble algorithm. Building upon Jiang and Layton's…
The chaotic nature of fluid flow and the uncertainties in initial conditions limit predictability. Small errors that occur in the initial condition can grow exponentially until they saturate at $\mathcal{O}$(1). Ensemble forecasting…
This paper presents and analyzes two robust, efficient, and optimally accurate fully discrete finite element algorithms for computing the parameterized Navier-Stokes Equations (NSEs) flow ensemble. The timestepping algorithms are…
We present an unconditionally energy-stable scheme for approximating the incompressible Navier-Stokes equations on domains with outflow/open boundaries. The scheme combines the generalized Positive Auxiliary Variable (gPAV) approach and a…
We present a generalized form of open boundary conditions, and an associated numerical algorithm, for simulating incompressible flows involving open or outflow boundaries. The generalized form represents a family of open boundary…
In this work we study different Implicit-Explicit (IMEX) schemes for incompressible flow problems with variable viscosity. Unlike most previous work on IMEX schemes, which focuses on the convective part, we here focus on treating parts of…
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier--Stokes equations. A semi-discrete entropy estimate for the entire…
This paper presents two algorithms for calculating an ensemble of solutions to laminar natural convection problems. The ensemble average is the most likely temperature distribution and its variance gives an estimate of prediction…
The paper presents numerical methods for unsteady flows of a viscous incompressible fluid in internal domains with many inlet/outlet sections. The novel variants of dissipative boundary conditions augmented by the inertia terms are used at…
We study topology optimization governed by the incompressible Navier-Stokes flows using a phase field model. Novel stabilized semi-implicit schemes for the gradient flows of Allen-Cahn and Cahn-Hilliard types are proposed for solving the…
This paper presents an algorithm for calculating an ensemble of solutions to natural convection problems. The ensemble average is the most likely temperature distribution and its variance gives an estimate of prediction reliability.…
The goal of this study is to develop an efficient numerical algorithm applicable to a wide range of compressible multicomponent flows. Although many highly efficient algorithms have been proposed for simulating each type of the flows, the…
Split form schemes for Euler and Navier-Stokes equations are useful for computation of turbulent flows due to their better robustness. This is because they satisfy additional conservation properties of the governing equations like kinetic…
We consider the Navier--Stokes--Fourier system in a bounded domain $\Omega \subset R^d$, $d=2,3$, with physically realistic in/out flow boundary conditions. We develop a new concept of weak solutions satisfying a general form of relative…
Euler--Euler or volume-averaged Navier--Stokes equations are used in various applications to model systems with two or more interpenetrating phases. Each fluid obeys its own momentum and mass equations, and the phases are typically coupled…
We present a new energy-stable open boundary condition, and an associated numerical algorithm, for simulating incompressible flows with outflow/open boundaries. This open boundary condition ensures the energy stability of the system, even…