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The inherent instability of oscillatory flows presents a significant challenge in microfluidics, impairing performance in different applications from particle detachemnt to organs-on-a-chip. Trapped air inside a microfluidic system…
This chapter concerns "control volume analysis", the standard engineering tool for the analysis of flow systems, and its application to entropy balance calculations. Firstly, the principles of control volume analysis are enunciated and…
This paper discusses the importance of high-frequency damping in high-order conservative finite-difference schemes for viscous terms in the Navier-Stokes equations. Investigating nonlinear instability encountered in a high-resolution…
A method for enhancing the stability and robustness of explicit schemes in computational fluid dynamics is presented. The method is based in reformulating explicit schemes in matrix form, which cane modified gradually into semi or…
We examine the stability of an Einstein-Maxwell perfect fluid configuration with a privileged direction of symmetry by means of a $1+1+2$-tetrad formalism. We use this formalism to cast, in a quasi linear symmetric hyperbolic form the…
The speed of sound in two-phase pipe flow systems is often several orders of magnitude greater than the travelling speed of hydraulic information (volume fractions.) Dynamically simulating such flows requires resolution of acoustic and…
For decades, uncertainty quantification techniques based on the spectral approach have been demonstrated to be computationally more efficient than the Monte Carlo method for a wide variety of problems, particularly when the dimensionality…
We consider a stabilized nonconforming finite element method for data assimilation in incompressible flow subject to the Stokes' equations. The method uses a primal dual structure that allows for the inclusion of nonstandard data. Error…
Many interesting physical problems described by systems of hyperbolic conservation laws are stiff, and thus impose a very small time-step because of the restrictive CFL stability condition. In this case, one can exploit the superior…
The computation of damping rates of an oscillating fluid with a free surface in which viscosity is small and surface tension high is numerically challenging. A typical application requiring such computation is drop-on-demand (DoD)…
We propose a novel decoupled unconditionally stable numerical scheme for the simulation of two-phase flow in a Hele-Shaw cell which is governed by the Cahn-Hilliard-Hele-Shaw system (CHHS) with variable viscosity. The temporal…
Symmetry reduction by the method of slices is applied to pipe flow in order to quotient the stream-wise translation and azimuthal rotation symmetries of turbulent flow states. Within the symmetry-reduced state space, all travelling wave…
Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics,…
Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and…
In this paper, the Entropically Damped Artificial Compressibility (EDAC) formulation of Clausen (2013) is used in the context of the Smoothed Particle Hydrodynamics (SPH) method for the simulation of incompressible fluids. Traditionally,…
A full viscous quantum hydrodynamic system for particle density, current density, energy density and electrostatic potential coupled with a Poisson equation in one dimensional bounded intervals is studied. First, the existence and…
This paper is devoted to the analysis of a numerical scheme for the coagulation and fragmentation equation with diffusion in space. A finite volume scheme is developed, based on a conservative formulation of the space nonhomogeneous…
In this article, we propose a novel conservative diffuse-interface method for the simulation of immiscible compressible two-phase flows. The proposed method discretely conserves the mass of each phase, momentum and total energy of the…
In Hamiltonian systems subjected to periodic perturbations the stable and unstable manifolds of the unstable periodic orbits provide the dynamical "skeleton" that drives the mixing process and bounds the chaotic regions of the phase space.…
We introduce new control-volume finite-element discretization schemes suitable for solving the Stokes problem. Within a common framework, we present different approaches for constructing such schemes. The first and most established strategy…