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Steady statistics of a passive scalar advected by a random two-dimensional flow of an incompressible fluid is described in the range of scales between the correlation length of the flow and the diffusion scale. That corresponds to the…
In this article we address flow problems that carry a multiscale character in time. In particular we consider the Navier-Stokes flow in a channel on a fast scale that influences the movement of the boundary which undergoes a deformation on…
We present a high-order method for flow simulation on unstructured curved nonconforming sliding meshes. This method utilizes dynamic transfinite mortar elements to exchange flow information between the two sides of a sliding interface. The…
We develop a model in two dimensions to characterise the growth rate of a tracer gradient mixed by a statistically homogeneous flow with rapid temporal variations. % % The model is based on the orientation dynamics of the passive-tracer…
We study the segregation of granular mixtures in two-dimensional silos using a set of coupled equations for surface flows of grains. We study the thick flow regime, where the grains are segregated in the rolling phase. We incorporate this…
Pure advection of a conservative scalar is relevant to several applications including two-phase flow. Successful numerical schemes must capture the sharp interface between the phases while maintaining a smooth (wrinkle-free) interfacial…
Engineered injection and extraction systems that create chaotic advection are promising procedures for enhancing mixing between two species. Mixing efficiencies vary considerably, so carefully selecting the design parameters, like pumping…
When polydisperse granular systems are sheared, the transverse dynamics is characterized by the interplay of size segregation and diffusion. Segregation in nonuniform and confined shearing flows is studied using annular shear cell…
We consider the negative regularity mixing properties of random volume preserving diffeomorphisms on a compact manifold without boundary. We give general criteria so that the associated random transfer operator mixes $H^{-\delta}$…
The problem of parameterizing the interactions of larger scales and smaller scales in fluid flows is addressed by considering a property of two-dimensional incompressible turbulence. The property we consider is selective decay, in which a…
Convergence failure and slow convergence rate are among the biggest challenges with solving the system of non-linear equations numerically. While using strictly small time steps sizes and unconditionally stable fully implicit scheme…
We report on the decay of a passive scalar in chaotic mixing protocols where the wall of the vessel is rotated, or a net drift of fluid elements near the wall is induced at each period. As a result the fluid domain is divided into a central…
We present faster algorithms for approximate maximum flow in undirected graphs with good separator structures, such as bounded genus, minor free, and geometric graphs. Given such a graph with $n$ vertices, $m$ edges along with a recursive…
In this paper a numerical procedure to simulate low diffusivity scalar turbulence is presented. The method consists of using a grid for the advected scalar with a higher spatial resolutions than that of the momentum. The latter usually…
We perform a convergence analysis of a discrete-in-time minimization scheme approximating a finite dimensional singularly perturbed gradient flow. We allow for different scalings between the viscosity parameter $\varepsilon$ and the time…
A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of…
Scene flow estimation is the task of describing 3D motion between temporally successive observations. This thesis aims to build the foundation for building scene flow estimators with two important properties: they are scalable, i.e. they…
The motions of a passive scalar $\hat{a}$ in a general high-frequency oscillating flow are studied. Our aim is threefold: (i) to obtain different classes of general solutions; (ii) to identify, classify, and develop related asymptotic…
Efficient particle sorting in microfluidic systems is vital for advancements in biomedical diagnostics and industrial applications. This study numerically investigates particle migration and passive sorting in symmetric serpentine…
Statistical properties of $d$-dimensional incompressible flows with and without cylindrical reduction are studied, leading to several explanations and conjectures about turbulent flows and passive scalars, such as the de-correlation between…