Related papers: A mixed formulation for a modification to Darcy eq…
We study the existence of solutions for Darcy's problem coupled with the heat equation under singular forcing; the right-hand side of the heat equation corresponds to a Dirac measure. The studied model allows thermal diffusion and viscosity…
In various applications, design problems involving structures and compliant mechanisms experience fluidic pressure loads. During topology optimization of such design problems, these loads adapt their direction and location with the…
The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…
A ubiquitous arrangement in nature is a free-flowing fluid coupled to a porous medium, for example a river or lake lying above a porous bed. Depending on the environmental conditions, thermal convection can occur and may be confined to the…
This paper investigates the theoretical implications of applying Darcy's law to premixed flames, a topic of growing interest in research on flame propagation in porous media and confined geometries. A multiple-scale analysis is carried out…
The two dimensional Navier-Stokes equation in a perforated domain with a dynamical slip boundary condition is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic…
In this paper, a strongly mass conservative and stabilizer free scheme is designed and analyzed for the coupled Brinkman-Darcy flow and transport. The flow equations are discretized by using a strongly mass conservative scheme in mixed…
A lack of regularity in the solution of the porous medium equation poses a serious challenge in its theoretical and numerical studies. A common strategy in theoretical studies is to utilize the pressure formulation of the equation where a…
We derive a novel and rigorous correction to the classical Reynolds lubrication approximation for fluids with viscosity depending upon the pressure. Our analysis shows that the pressure dependence of viscosity leads to additional nonlinear…
The coupled Darcy-Stokes problem is widely used for modeling fluid transport in physical systems consisting of a porous part and a free part. In this work we consider preconditioners for monolitic solution algorithms of the coupled…
Topology optimization offers optimal material layouts, enabling automation in the design of devices. Given the recent advances in computer technology and additive manufacturing, topology optimization is increasingly being used to design…
In this work we propose tailored model order reduction for varying boundary optimal control problems governed by parametric partial differential equations. With varying boundary control, we mean that a specific parameter changes where the…
In this paper, we conduct a numerical analysis of the strong stabilization and polynomial decay of solutions for the initial boundary value problem associated with a system that models the dynamics of a mixture of two rigid solids with…
Matrix acidization simulation is a challenging task in the study of flows in porous media, due to the changing porosity in the procedure. The improved DBF framework is one model to do this simulation, and its numerical scheme discretises…
This paper focuses on discussing Newton's method and its hybrid with machine learning for the steady state Navier-Stokes Darcy model discretized by mixed element methods. First, a Newton iterative method is introduced for solving the…
We develop a unified continuum modeling framework for viscous fluids and hyperelastic solids using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the…
In this paper we develop an a priori error analysis of a new unified mixed finite element method for the coupling of fluid flow with porous media flow in $\mathbb{R}^N$, $N\in\{2,3\}$ on isotropic meshes. Flows are governed by the Stokes…
Equations governing the flow of a polar fluid, with pressure-dependent Newtonian viscosity, through a variable-porosity medium are developed. Averaged equations are obtained using intrinsic volume averaging. A drag function is introduced to…
We perform linear and nonlinear stability analysis for thermal convection in a fluid overlying a saturated porous medium. We use a coupled system, with the Navier-Stokes equations and Darcy's equation governing the free-flow and the porous…
Climate change and global warming are among the most significant issues that humanity is currently facing, and also among the issues that pose the greatest threats to all mankind. These issues are primarily driven by abnormal increases in…