Related papers: A numerical model based on the curvilinear coordin…
Investigating blood flow in the cardiovascular system is crucial for assessing cardiovascular health. Computational approaches offer some non-invasive alternatives to measure blood flow dynamics. Numerical simulations based on traditional…
The computation of flows with large density contrasts is notoriously difficult. To alleviate the difficulty we consider a discretization of the Navier-Stokes equation that advects mass and momentum in a consistent manner. Incompressible…
We study a nonlinear, unsteady, moving boundary, fluid-structure interaction (FSI) problem arising in modeling blood flow through elastic and viscoelastic arteries. The fluid flow, which is driven by the time-dependent pressure data, is…
When studying fluid mechanics in terms of instability, bifurcation and invariant solutions one quickly finds out how little can be done by pen and paper. For flows on sufficiently simple domains and under sufficiently simple boundary…
The system of Navier--Stokes--Fourier equations is one of the most celebrated systems of equations in modern science. It describes dynamics of fluids in the limit when gradients of density, velocity and temperature are sufficiently small,…
We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed…
In this study the numerical performance of the fourth order compact formulation of the steady 2-D incompressible Navier-Stokes equations introduced by Erturk et al. (Int. J. Numer. Methods Fluids, 50, 421-436) will be presented. The…
Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. This makes such methods especially suitable for two-way coupled flow-body problems, where the body mechanics are partially driven by…
The mathematical formulation, basic concept and numerical implementation of a new meshless method for solving three dimensional fluid flow and related heat transfer problems are presented in this paper. Moving least squares approximation is…
This paper presents a numerical method based on the variational quantum algorithm to solve potential and Stokes flow problems. In this method, the governing equations for potential and Stokes flows can be respectively written in the form of…
We study convergence of a finite volume scheme for the Navier-Stokes-Fourier system describing the motion of compressible viscous and heat conducting fluids. The numerical flux uses upwinding with an additional numerical diffusion of order…
A well-established numerical approach to solve the Navier--Stokes equations for incompressible fluids is Chorin's projection method, whereby the fluid velocity is explicitly updated, and then an elliptic problem for the pressure is solved,…
We develop a Bayesian methodology for numerical solution of the incompressible Navier--Stokes equations with quantified uncertainty. The central idea is to treat discretized Navier--Stokes dynamics as a state-space model and to view…
The simulation of fluid flow problems, specifically incompressible flows governed by the Navier-Stokes equations (NSE), holds fundamental significance in a range of scientific and engineering applications. Traditional numerical methods…
We prove the existence of martingale solutions to a stochastic fluid-structure interaction problem involving a viscous, incompressible fluid flow, modeled by the Navier-Stokes equations, through a deformable elastic tube modeled by…
Numerical simulations for flow and transport in subsurface porous media often prove computationally prohibitive due to property data availability at multiple spatial scales that can vary by orders of magnitude. A number of model order…
In the present thesis, we are interested in the description of the dynamics of flows on large scales. In this context, the fluids are governed by rotational, weak compressibility and stratification effects, whose importance is measured by…
The authors have discussed the method and merit of introducing the curvilinear coordinates into numerical analysis and have shown some numerical examples. However, they used analytical functions for the mappings in the examples and didn't…
This work presents a novel numerical investigation of the dynamics of free-boundary flows of viscoelastic liquid membranes. The governing equation describes the balance of linear momentum, in which the stresses include the viscoelastic…
The paper studies the equilibrium configurations of inextensible elastic membranes exhibiting lateral fluidity. Using a continuum description of the membrane's motions based on the surface Navier--Stokes equations with bending forces, the…