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A mathematical model that governs turbulent flows through permeable media is considered in this work. The model under consideration is based on a double-averaging concept which in turn is described by the time-averaging technique…
The appropriate boundary condition between an unconfined incompressible viscous fluid and a porous medium is given by the law of Beavers and Joseph. The latter has been justified both experimentally and mathematically, using the method of…
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…
The computational modeling of high-speed flows (e.g. hypersonic) and space plasmas is characterized by a plethora of complex physical phenomena, in particular involving strong oblique shocks, bow shocks and/or shock waves boundary layer…
Diffusive molecular dynamics is a novel model for materials with atomistic resolution that can reach diffusive time scales. The main ideas of diffusive molecular dynamics are to first minimize an approximate variational Gaussian free energy…
In this paper, the physics of flow instability and turbulent transition in shear flows is studied by analyzing the energy variation of fluid particles under the interaction of base flow with a disturbance. For the first time, a model…
The paper develops a method for the numerical simulation of a free-surface flow of incompressible viscous fluid around a streamlined body. The body is a rigid stationary construction partially submerged in the fluid. The application we are…
Higher-order numerical methods are used to find accurate numerical solutions to hyperbolic partial differential equations and equations of transport type. Limiting is required to either converge to the correct type of solution or to adhere…
We present a new rigorous method for estimating statistical quantities in fluid dynamics such as the (average) energy dissipation rate directly from the equations of motion. The method is tested on shear flow, channel flow,…
The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid-structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an…
Simulations of motion by mean curvature in bounded domains, with applications to bubble motion and grain growth, rely upon boundary conditions that are only approximately compatible with the equation of motion. Three closed form solutions…
Thermo-osmotic and related thermo-phoretic phenomena can be found in many situations from biology to colloid science, but the underlying molecular mechanisms remain largely unexplored. Using molecular dynamics simulations, we measured the…
We introduce a new consensus based optimization (CBO) method where interacting particle system is driven by jump-diffusion stochastic differential equations. We study well-posedness of the particle system as well as of its mean-field limit.…
Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in…
We show that capillary waves can exist at the the boundary between miscible co-flowing fluids. We unveil that the interplay between transient interfacial stresses and confinement drives the progressive transition from the well-known…
In this paper we propose and study a curvature-based mathematical model for dorsal closure in embryonic drosophila. Using an analysis that mixes maximum-principle and integral-estimates, we establish global existence and convergence for…
A closed-form analytical solution is found for the nonlinear dynamics of isolated, near-threshold waves in the presence of strong scattering. The proposed solution can be useful in verifying codes across several disciplines, including…
This work presents a robust and efficient sharp interface immersed boundary (IBM) framework, which is applicable for all-speed flow regimes and is capable of handling arbitrarily complex bodies (stationary or moving). The work deploys an…
This article proposes a Variational Quantum Algorithm to solve linear and nonlinear thermofluid dynamic transport equations. The hybrid classical-quantum framework is applied to problems governed by the heat, wave, and Burgers' equation in…
The boundary conditions at the deformable interface between two contacting fluids are derived for the general case of the large-amplitude perturbations. The interface is modeled as perturbed free boundary that evolves in time, and the…