Related papers: Robust and efficient identification of optimal mix…
For elliptic interface problems in two- and three-dimensions with a possible very low regularity, this paper establishes a priori error estimates for the Raviart-Thomas and Brezzi-Douglas-Marini mixed finite element approximations. These…
We study gravitationally unstable, transient, diffusive boundary layers in porous media using modal and nonmodal stability methods. Using nonmodal stability theory, we demonstrate that both the onset of linear instabilities and the shape of…
Incompressible flows can be effective mixers by appropriately advecting a passive tracer to produce small filamentation length scales. In addition, diffusion is generally perceived as beneficial to mixing due to its ability to homogenise a…
We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive…
We investigate the mixing properties of scalars stirred by spatially smooth, divergence-free flows and maintained by a steady source-sink distribution. We focus on the spatial variation of the scalar field, described by the {\it dissipation…
In this paper a new primal-dual mixed finite element method is introduced, aimed to model multiscale problems with several geometric subregions in the domain of interest. In each of these regions porous media fluid flow takes place, but…
This paper is concerned with the transition of the laminar flow in a duct of square cross-section. Like in the similar case of the pipe flow, the motion is linearly stable for all Reynolds numbers, rendering this flow a suitable candidate…
Empirical observations show that turbulence exhibits a broad range of scaling exponents, characterizing how the velocity gradients diverge in the inviscid limit. These exponents are thought to be linked to singular solutions of the Euler…
We introduce a general-purpose method for optimising the mixing rate of advective fluid flows. An existing velocity field is perturbed in a $C^1$ neighborhood to maximize the mixing rate for flows generated by velocity fields in this…
Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…
The mixing of an impurity into a flowing fluid is an important process in many areas of science, including geophysical processes, chemical reactors, and microfluidic devices. In some cases, for example periodic flows, the concepts of…
A passive scalar is advected by a velocity field, with a nonuniform spatial source that maintains concentration inhomogeneities. For example, the scalar could be temperature with a source consisting of hot and cold spots, such that the mean…
The numerical simulation of multiphase flows involving dispersed components with large scale disparities, such as the collisions between millimeter-sized bubbles and micron-sized mineral particles in flotation, poses a significant…
The design of an experiment, e.g., the setting of initial conditions, strongly influences the accuracy of the whole process of determining model parameters from data. We impose a sensitivity-based approach for choosing optimal design…
We consider the numerical approximation of compressible flow in a pipe network. Appropriate coupling conditions are formulated that allow us to derive a variational characterization of solutions and to prove global balance laws for the…
Mathematical models for flow through porous media typically enjoy the so-called maximum principles, which place bounds on the pressure field. It is highly desirable to preserve these bounds on the pressure field in predictive numerical…
We consider primal-dual mixed finite element methods for the advection--diffusion equation. For the primal variable we use standard continuous finite element space and for the flux we use the Raviart-Thomas space. We prove optimal a priori…
Data flow analysis and optimization is considered for homogeneous rectangular mesh networks. We propose a flow matrix equation which allows a closed-form characterization of the nature of the minimal time solution, speedup and a simple…
A change of solute dispersion regime with the flow velocity has been studied both at the macroscopic and pore scales in a transparent array of capillary channels using an optical technique allowing for simultaneous local and global…
Physical dynamic networks most commonly consist of interconnections of physical components that can be described by diffusive couplings. These diffusive couplings imply that the cause-effect relationships in the interconnections are…