Related papers: A numerical model based on the curvilinear coordin…
In this paper, we develop a new mass conservative numerical scheme for the simulations of a class of fluid-structure interaction problems. We will use the immersed boundary method to model the fluid-structure interaction, while the fluid…
Coupled systems of free flow and porous media arise in a variety of technical and environmental applications. For laminar flow regimes, such systems are described by the Stokes equations in the free-flow region and Darcy's law in the porous…
This work develops and analyzes a variational-monolithic unfitted finite element formulation of a linear fluid-structure interaction problem in Eulerian coordinates with a fixed interface. The overall discretization is based on a backward…
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…
Fluid flow applications can involve a number of coupled problems. One is the simulation of free-surface flows, which require the solution of a free-boundary problem. Within this problem, the governing equations of fluid flow are coupled…
This report presents a low computational and cognitive complexity, stable, time accurate and adaptive method for the Navier-Stokes equations. The improved method requires a minimally intrusive modification to an existing program based on…
Computational fluid dynamics lies at the heart of many issues in science and engineering, but solving the associated partial differential equations remains computationally demanding. With the rise of quantum computing, new approaches have…
In this paper, we present an efficient numerical algorithm for solving the time-dependent Cahn--Hilliard--Navier--Stokes equations that model the flow of two phases with different densities. The pressure-correction step in the projection…
We show that an attempt to compute numerically a viscous flow in a domain with a piece-wise smooth boundary by straightforwardly applying well-tested numerical algorithms (and numerical codes based on their use, such as COMSOL Multiphysics)…
A novel algorithm for the direct numerical simulation of the variable-density, low-Mach Navier-Stokes equations extending the method of Kim, Moin, and Moser (1987) for incompressible flow is presented here. A Fourier representation is…
We perform numerical analysis of a nonlinear gradient flow, which can be regarded as a parabolic minimal surface problem or a regularised total variation flow, using the gradient discretisation method (GDM). GDM is a unified convergence…
The finite cell method (FCM) belongs to the class of immersed boundary methods, and combines the fictitious domain approach with high-order approximation, adaptive integration and weak imposition of unfitted Dirichlet boundary conditions.…
Multiphase, compressible and viscous flows are of crucial importance in a wide range of scientific and engineering problems. Despite the large effort paid in the last decades to develop accurate and efficient numerical techniques to address…
We consider a class of Fuchsian equations that, for instance, describes the evolution of compressible fluid flows on a cosmological spacetime. Using the method of lines, we introduce a numerical algorithm for the singular initial value…
Use of curvilinear coordinates is sometimes indicated by the inherent geometry of a fluid dynamics problem, but this introduces fictitious forces into the momentum equations that spoil strict conservative form. If one is willing to work in…
A new arbitrary Lagrangian-Eulerian (ALE) formulation for Navier-Stokes flow on self-evolving surfaces is presented. It is based on a general curvilinear surface parameterization that describes the motion of the ALE frame. Its in-plane part…
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
An alternative form of the general solution of the linearized stationary Navier-Stokes equations for an incompressible fluid in spherical coordinates is obtained by the vector potential method. A previously published solution to this…
In this work, we develop a cut-based unfitted finite element formulation for solving nonlinear, nonstationary fluid-structure interaction with contact in Eulerian coordinates. In the Eulerian description fluid flow modeled by the…