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Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. This makes such methods especially suitable for two-way coupled flow-body problems, where the body mechanics are partially driven by…
Recently, the intrinsic sampling method has been developed in order to obtain, from molecular simulations, the intrinsic structure of the liquid-vapor interface that is presupposed in the classical capillary wave theory. Our purpose here is…
In this paper, we present a second-order accurate finite-difference method for solving convectiondiffusion equations with interfacial jumps on a moving interface. The proposed method is constructed under a semi-Lagrangian framework for…
In this paper we propose a new diffuse interface model for the numerical simulation of inviscid compressible flows around fixed and moving solid bodies of arbitrary shape. The solids are assumed to be moving rigid bodies, without any…
We present a full classification of the short-time behaviour of the interfaces and local solutions to the nonlinear parabolic $p$-Laplacian type reaction-diffusion equation of non-Newtonian elastic filtration \[…
Interactions between an evolving solid and inviscid flow can result in substantial computational complexity, particularly in circumstances involving varied boundary conditions between the solid and fluid phases. Examples of such…
We present an extension of the Piecewise Parabolic Method to special relativistic fluid dynamics in multidimensions. The scheme is conservative, dimensionally unsplit, and suitable for a general equation of state. Temporal evolution is…
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…
An interface control principle is proposed for unsteady fluid-structure in- teraction (FSI) analyses. This principle introduces a method of explicitly controlling the interface motion in the temporal direction to minimize the residual force…
This work has explored interface evolution and pinch-off mechanism of the droplet formation in two-phase flow through cross-flow microfluidic device. The two-dimensional mathematical model equations have been solved using the finite element…
Capillarity-driven self-assembly at fluidic interfaces offers a scalable route to large, reconfigurable materials. Microscale particles with high horizontal-to-vertical aspect ratios become attractive building blocks for shape-directed…
The dynamics of compressible liquid-vapor flow depends sensitively on the microscale behavior at the phase boundary. We consider a sharp-interface approach, and propose a multiscale model to describe liquid-vapor flow accurately, without…
The numerical simulation of wetting and dewetting of geometrically complex surfaces benefits from unstructured numerical methods because they discretize the domain with second-order accuracy. A recently developed unstructured geometric…
We introduce a fast and robust algorithm for finding a plane $\Gamma$ with given normal $\vec{n}_\Gamma$, which truncates an arbitrary polyhedron $\mathcal{P}$ such that the remaining sub-polyhedron admits a given volume…
This paper proposes an approach combining the Volume Penalization (VP) and the the Lattice Boltzmann method (LBM) to compute fluid structure interaction involving rigid bodies. The method consists in adding a force term in the LBM…
Particle Imaging Velocimetry (PIV) estimates the flow of fluid by analyzing the motion of injected particles. The problem is challenging as the particles lie at different depths but have similar appearance and tracking a large number of…
The flow near a moving contact line is primarily governed by three key parameters: viscosity ratio, dynamic contact angle, and inertia. While the behavior of dynamic contact angles has been extensively studied in earlier experimental and…
The moment-of-fluid method (MOF) is known as an extension of the volume-of-fluid method with piecewise linear interface construction (VOF-PLIC). In this study, several directional splitting advection algorithms are extended from the…
We study some numerical methods for solving second order elliptic problem with interface. We introduce an immersed interface finite element method based on the `broken' $P_1$-nonconforming piecewise linear polynomials on interface…
In this work, physics-informed neural networks are applied to incompressible two-phase flow problems. We investigate the forward problem, where the governing equations are solved from initial and boundary conditions, as well as the inverse…