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This paper proposes a novel robust model predictive control (RMPC) method for the stabilization of constrained systems subject to additive disturbance (AD) and multiplicative disturbance (MD). Concentric containers are introduced to…
Traditional finite element approaches are well-known to introduce spurious oscillations when applied to advection-dominated problems. We explore alleviation of this issue from the perspective of a generalized finite element formulation,…
We propose and analyze a new method for the unsteady incompressible magnetohydrodynamics equations on convex domains with hybrid approximations of both vector-valued and scalar-valued fields. The proposed method is convection-semirobust,…
We present three new semi-Lagrangian methods based on radial basis function (RBF) interpolation for numerically simulating transport on a sphere. The methods are mesh-free and are formulated entirely in Cartesian coordinates, thus avoiding…
Meshfree methods based on radial basis function (RBF) approximation are of interest for numerical solution of partial differential equations (PDEs) because they are flexible with respect to the geometry of the computational domain, they can…
We present a unified numerical method to determine the shapes of multiple Hele-Shaw bubbles in steady motion, and in the absence of surface tension, in three planar domains: free space, the upper half-plane, and an infinite channel. Our…
In this paper we study a system of advection-diffusion equations in a bulk domain coupled to an advection-diffusion equation on an embedded surface. Such systems of coupled partial differential equations arise in, for example, the modeling…
This paper proposes two contributions to the calculation of free surface flows using the particle finite element method (PFEM). The PFEM is based on a Lagrangian approach: a set of particles defines the fluid. Then, unlike a pure Lagrangian…
The finite difference time domain method is one of the simplest and most popular methods in computational electromagnetics. This work considers two possible ways of generalising it to a meshless setting by employing local radial basis…
Enhancing the efficiency of water electrolysis, which can be severely impacted by the nucleation and growth of bubbles, is key in the energy transition. In this combined experimental and numerical study, in-situ bubble evolution and…
We consider the a posteriori error estimation for convection-diffusion-reaction equations in both diffusion-dominated and convection/reaction-dominated regimes. We present an explicit hybrid estimator, which, in each regime, is proved to be…
A novel theoretical model for bubble dynamics is established that simultaneously accounts for the liquid compressibility, phase transition, oscillation, migration, ambient flow field, etc. The bubble dynamics equations are presented in a…
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…
The rise of a single bubble confined between two vertical plates is investigated over a wide range of Reynolds numbers. In particular, we focus on the evolution of the bubble speed, aspect ratio and drag coefficient during the transition…
The advantage of particle Lagrangian methods in computational fluid dynamics is that advection is accurately modeled. However, this complicates the calculation of space derivatives. If a mesh is employed, it must be updated at each time…
Understanding how substrate-attached bubbles respond to ultrasound is important for applications from industrial cleaning to biomedical therapy. Under ultrasonic excitation, bubbles can deform through Faraday instability and periodically…
We propose an improved viscosity model accounting for experiments of emulsions of two immiscible liquids at arbitrary volume fractions and low shear rates. The model is based on a recursive-differential method formulated in terms of the…
A theoretical formulation is proposed for forced mass transport by pressure gradients in a liquid binary mixture around a spherical bubble undergoing volume oscillations in a sound field. Assuming the impermeability of the bubble wall to…
This paper focuses on RBF-based meshless methods for approximating differential operators, one of the most popular being RBF-FD. Recently, a hybrid approach was introduced that combines RBF interpolation and traditional finite difference…
Non-linear equations of radial motion of a gas bubble in a compressible viscous liquid have been modified considering effects of viscosity and compressibility more complete than all previous works. A new set of equations has been derived…