Related papers: A study on boundary separation in an idealized oce…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
We develop a parameter-free model for the fragmentation of drops colliding off-center. The prediction is excellent over a wide range of liquid properties. The so-called stretching separation is attributed to the extension of the merged drop…
The Immersed Boundary Method (IBM) is one of the popular one-fluid mixed Eulerian-Lagrangian methods to simulate motion of droplets. While the treatment of a moving complex boundary is an extremely time consuming and formidable task in a…
This paper presents an edge detection method based on global and local parameters of the image, which produces satisfactory results on the edge detection of complex images and has a simple structure for execution. The local and global…
Shape estimation and object reconstruction are common problems in image analysis. Mathematically, viewing objects in the image plane as random sets reduces the problem of shape estimation to inference about sets. Currently existing…
The simulation of large open water surface is challenging using a uniform volumetric discretization of the Navier-Stokes equations. Simulating water splashes near moving objects, which height field methods for water waves cannot capture,…
Flow in fractured porous media represents a challenge for discretization methods due to the disparate scales and complex geometry. Herein we propose a new discretization, based on the mixed finite element method and mortar methods. Our…
The goal of the present work is to solve a linear dispersive equation with variable coefficient advection on an unbounded domain. In this setting, transparent boundary conditions are vital to allow waves to leave (or even re-enter) the,…
We consider an optimal recovery problem for the Poisson problem when the boundary data is unknown. Compensating information is provided in the form of a finite number of measurements of the solution. A finite element algorithm for this…
We study the half-plane problem for the elastic wave equation subject to a free surface boundary condition, with particular emphasis on almost incompressible materials. A normal mode analysis is developed to estimate the solution in terms…
Method-of-lines discretizations are demanding test problems for stiff integration methods. However, for PDE problems with known analytic solution the presence of space discretization errors or the need to use codes to compute reference…
In a recent paper as an alternative to models based on the notion of ideal mathematical point, characterized by a property of separatedness, we considered a viewpoint based on the notion of continuous change, making use of elements of a…
Most recent advances in machine learning and analytics for process control pose the question of how to naturally integrate new data-driven methods with classical process models and control. We propose a process modeling framework enabling…
The dispersion curves of (elastic) waveguides frequently exhibit crossings and osculations (also known as veering, repulsion, or avoided crossing). Osculations are regions in the dispersion diagram where curves approach each other…
Engineering simulations using boundary-value partial differential equations often implicitly assume that the uncertainty in the location of the boundary has a negligible impact on the output of the simulation. In this work, we develop a…
Many mathematical models utilize limit processes. Continuous functions and the calculus, differential equations and topology, all are based on limits and continuity. However, when we perform measurements and computations, we can achieve…
Solutions of initial-boundary value problems for systems of conservation laws depend on the underlying viscous mechanism, namely different viscosity operators lead to different limit solutions. Standard numerical schemes for approximating…
Accurate representation of large-scale flow patterns in low-resolution ocean simulations is one of the most challenging problems in ocean modelling. The main difficulty is to correctly reproduce effects of unresolved small scales on the…
The increasing prevalence of marine pollution during the past few decades motivated recent research to help ease the situation. Typical water quality assessment requires continuous monitoring of water and sediments at remote locations with…
We present a collision model for phase-resolved Direct Numerical Simulations of sediment transport that couple the fluid and particles by the Immersed Boundary Method. Typically, a contact model for these types of simulations comprises a…