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Granular dynamics driven by fluid flow is ubiquitous in many industrial and natural processes, such as fluvial and coastal sediment transport. Yet, their complex multiphysics nature challenges the accuracy and efficiency of numerical…
We consider the 3D compressible isentropic Euler equations describing the motion of a liquid in an unbounded initial domain with a moving boundary and a fixed flat bottom at finite depth. The liquid is under the influence of gravity and…
A novel centrifuge set-up for the study of unsaturated flow characteristics in porous media is examined. In this set-up, simple boundary conditions can be used, but a free moving boundary between unsaturated-saturated flow arises. A precise…
Considering the isentropic Euler equations of compressible fluid dynamics with geometric effects included, we establish the existence of entropy solutions for a large class of initial data. We cover fluid flows in a nozzle or in spherical…
This paper presents a variational approach to doubly-nonlinear (gradient) flows (P) of nonconvex energies along with nonpotential perturbations (i.e., perturbation terms without any potential structures). An elliptic-in-time regularization…
Applied problems of oil and gas recovery are studied numerically using the mathematical models of multiphase fluid flows in porous media. The basic model includes the continuity equations and the Darcy laws for each phase, as well as the…
We present a new second order accurate structure-preserving finite volume scheme for the solution of the compressible barotropic two-phase model of Romenski et. al in multiple space dimensions. The governing equations fall into the wider…
The immersed boundary method is a mathematical formulation and numerical method for solving fluid-structure interaction problems. For many biological problems, such as models that include the cell membrane, the immersed structure is a…
The numerical simulation of fluid flow through a complex geometry with heat transfer is of strong interest for many applications, such as oil-filled power transformers. A fundamental challenge here is that high resolution is necessary to…
The heterogeneous distribution of water-repellent materials at the soil surface causes a phenomenon known as fractional wettability. This condition frequently triggers destabilization of the wetting front during water infiltration,…
We study the dynamics of a droplet moving on an inclined rough surface in the absence of inertial and viscous stress effects. In this case, the dynamics of the droplet is a purely geometric motion in terms of the wetting domain and the…
Standard finite element discretizations of the Richards equation may violate the discrete minimum principle, producing unphysical negative saturations. While existing bound-preserving methods typically rely on computationally expensive…
The problem of two-phase flow in straight capillaries of polygonal cross section displays many of the dynamic characteristics of rapid interfacial motions associated with pore-scale displacements in porous media. Fluid inertia is known to…
In this study, we develop computational models and methodology for accurate multi-component-flow simulation in under-resolved multi-scale porous structures. It is generally impractical to fully resolve the flow in porous structures with…
In this paper we introduce an optimal control approach to Richards' equation in an irrigation framework, aimed at minimizing water consumption while maximizing root water uptake. We first describe the physics of the nonlinear model under…
In this paper, we investigate the prescribed total geodesic curvature problem for generalized circle packing metrics in hyperbolic background geometry on surfaces with infinite cellular decompositions. To address this problem, we introduce…
We perform high-order simulations of two-phase flows in capillaries, with and without evaporation. Since a sharp-interface model is used, singularities can arise at the three-phase contact line, where the fluid-fluid interface interacts…
Multiphase flow in porous media occurs in several disciplines including petroleum reservoir engineering, petroleum systems' analysis, and CO$_2$ sequestration. While simulations often use a fully implicit discretization to increase the time…
In this paper, we propose a method of fundamental solutions for the problems of two-dimensional potential flow past a doubly-periodic array of obstacles. The solutions of these problems involve doubly-periodic functions, and it is difficult…
The inviscid multi-layer quasi-geostrophic equations are considered over an arbitrary bounded domain. The no-flux but non-homogeneous boundary conditions are imposed to accommodate the free fluctuations of the top and layer interfaces.…