Related papers: Parallel Domain Decomposition method for the fully…
In this paper we consider the flow of two incompressible, viscous and immiscible fluids in a bounded domain, with different densities and viscosities. This model consists of a coupled system of Navier-Stokes and Mullins-Sekerka type parts,…
This paper is concerned with the numerical solution of porous-media flow and transport problems , i. e. heterogeneous, advection-diffusion problems. Its aim is to investigate numerical schemes for these problems in which different time…
The Immersed Boundary method has evolved into one of the most useful computational methods in studying fluid structure interaction. On the other hand, the Immersed Boundary method is also known to suffer from a severe timestep stability…
We consider a compressible Stokes problem in the quasi-stationary case coupled with a time dependent advection-diffusion equation with special emphasis on high viscosity contrast geophysical mantle convection applications. In space, we use…
We present a parallel-scalable method for simulating non-dilute suspensions of deformable particles immersed in Stokesian fluid in three dimensions. A critical component in these simulations is robust and accurate collision handling. This…
In this paper we show and discuss the use of a versatile interaction potential approach coupled with an immersed boundary method to simulate a variety of flows involving deformable bodies. In particular, we focus on two kinds of problems,…
In this article, a two-level overlapping domain decomposition preconditioner is developed for solving linear algebraic systems obtained from simulating Darcy flow in high-contrast media. Our preconditioner starts at a mixed finite element…
This paper presents and evaluates a framework for the coupling of subdomain-local projection-based reduced order models (PROMs) using the Schwarz alternating method following a domain decomposition (DD) of the spatial domain on which a…
We propose a decoupled divergence-free neural networks basis (Decoupled-DFNN) method for solving incompressible flow problems, including the Stokes and Navier-Stokes equations. To ensure the divergence free property exactly, the velocity…
In this work, we present a mathematical and computational framework to model the dynamics of open lipid bilayer membranes interacting with ambient Stokes flow. The model explicitly couples the three-dimensional viscous fluid, the…
The Classic Howard's algorithm, a technique of resolution for discrete Hamilton-Jacobi equations, is of large use in applications for its high efficiency and good performances. A special beneficial characteristic of the method is the…
In this paper, we are concerned with the global pressure formulation of immiscible incompressible two-phase flow between different rock types. We develop for this problem two robust schemes based on domain decomposition (DD) methods and…
We introduce a coupled system of PDEs for the modeling of the fluid-fluid and fluid-solid interaction in a poroelastic material with a single static fracture. The fluid flow in the fracture is modeled by a lower-dimensional Darcy equation,…
Three algorithms are developed for uncertainty quantification in modeling coupled Stokes and Darcy flows. The porous media may consist of multiple regions with different properties. The permeability is modeled as a non-stationary stochastic…
A new diffuse interface model has been proposed in this study for simulating binary alloy solidification under universal cooling conditions, involving both equilibrium and non-equilibrium solute partitioning. Starting from the Gibbs-Thomson…
Parabolic equations on evolving domains model a multitude of applications including various industrial processes such as the molding of heated materials. Such equations are numerically challenging as they require large-scale computations…
We consider sequential and parallel decomposition methods for a dual problem of a general total variation minimization problem with applications in several image processing tasks, like image inpainting, estimation of optical flow and…
Performing highly accurate simulations of droplet systems is a challenging problem. This is primarily due to the interface dynamics which is complicated further by the addition of surfactants. This paper presents a boundary integral method…
As the number of processor cores on supercomputers becomes larger and larger, algorithms with high degree of parallelism attract more attention. In this work, we propose a novel space-time coupled algorithm for solving an inverse problem…
In this paper we advance the analysis of discretizations for a fluid-structure interaction model of the monolithic coupling between the free flow of a viscous Newtonian fluid and a deformable porous medium separated by an interface. A…