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Modeling and a Domain Decomposition Method with Finite Element Discretization for Coupled Dual-Porosity Flow and Navier–Stokes Flow
In this paper, we first propose and analyze a steady state Dual-Porosity-Navier–Stokes model, which describes both Dual-Porosity flow and free flow...
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Robin-Robin domain decomposition methods for the dual-porosity-conduit system
The recently developed dual-porosity-Stokes model describes a complicated dual-porosity-conduit system which uses a dual-porosity/permeability model...
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Global Well-Posedness of an Initial-Boundary Value Problem of the 2-D Incompressible Navier-Stokes-Darcy System
We investigate in the paper the initial boundary value problem of the two dimensional incompressible Navier-Stokes-Darcy system in a strip domain. It...
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Multiscale Approach for Modeling Multiphase Fluid Flows in Installations for Reprocessing of Natural Gas
AbstractThe work is devoted to the development of a multiscale approach for modeling multiphase liquid and gas flows in a porous medium. The problem...
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On the Doubly Non-local Hele-Shaw–Cahn–Hilliard System: Derivation and 2D Well-Posedness
Starting from a classic non-local (in space) Cahn–Hilliard–Stokes model for two-phase flow in a thin heterogeneous fluid domain, we rigorously derive...
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A Numerical Algorithm Based on Probing to Find Optimized Transmission Conditions
Optimized Schwarz Methods (OSMs) are very versatile: they can be used with or without overlap, converge faster compared to other domain decomposition...
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Tumor Evolution Models of Phase-Field Type with Nonlocal Effects and Angiogenesis
In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models...
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Highly efficient and unconditionally energy stable semi-discrete time-marching numerical scheme for the two-phase incompressible flow phase-field system with variable-density and viscosity
For the variable-density/viscosity Cahn-Hilliard phase-field model of the binary-phase incompressible fluid flow system, the development of...
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Stability Analysis of Coupled Advection-Diffusion Models with Bulk Interface Condition
Numerical stability is of critical importance in general circulation models because it affects the design of algorithms, time to solution, and...
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A new local projection stabilization virtual element method for the Oseen problem on polygonal meshes
For the Oseen problem, we present a new stabilized virtual element method on polygonal meshes that allows us to employ “equal-order” virtual element...
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A Two-Grid Decoupled Algorithm for a Multi-Dimensional Darcy–Brinkman Fracture Model
In this paper, we study numerical methods for solving a multi-dimensional fracture model, which couples n -dimensional Darcy flow in matrix with
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Projection Based Semi-Implicit Partitioned Reduced Basis Method for Fluid-Structure Interaction Problems
In this manuscript a POD-Galerkin based Reduced Order Model for unsteady Fluid-Structure Interaction problems is presented. The model is based on a...
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A comparative study of integral and coupled approaches for modeling hydraulic exchange processes across a rippled streambed
Although both are crucial parts of the hydrological cycle, groundwater and surface water had traditionally been addressed separately. In recent...
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Parameter-robust preconditioners for Biot’s model
This work presents an overview of the most relevant results obtained by the authors regarding the numerical solution of the Biot’s consolidation...
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An Investigation of Information Flux between Turbulent Boundary Layer and Porous Medium
The interaction between boundary layer turbulence and a porous layer is the cornerstone to the interface engineering. In this study, the spatial...
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Is Minimising the Convergence Rate a Good Choice for Efficient Optimized Schwarz Preconditioning in Heterogeneous Coupling? The Stokes-Darcy Case
Optimized Schwarz Methods (OSM) are domain decomposition techniques based on Robin-type interface condition that have become increasingly popular in...
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Pressure-Tight and Non-stiff Volume Penalization for Compressible Flows
Embedding geometries in structured grids allows a simple treatment of complex objects in fluid simulations. Various methods for embedding geometries...
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Multiphase Models for Moving Boundary Problems in Biology
We address the modelling of tissue deformation using mixture theory. The governing equations consist of mass and momentum balances for two phases,...
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Porous Materials
A porous material is a substance that contains pores, or spaces, between solid materials through which liquid or gas can flow. Examples of naturally...
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Fully-Decoupled and Second-Order Time-Accurate Scheme for the Cahn–Hilliard Ohta–Kawaski Phase-Field Model of Diblock Copolymer Melt Confined in Hele–Shaw Cell
In this work, we consider numerical approximations of the phase-field model of diblock copolymer melt confined in Hele–Shaw cell, which is a very...
