Related papers: An implicit boundary integral method for interface…
A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial…
The Stefan problem is a classical free-boundary problem that models phase-change processes and poses computational challenges due to its moving interface and nonlinear temperature-phase coupling. In this work, we develop a physics-informed…
Imposition of free slip boundary conditions in science and engineering simulations presents a challenge when the simulation domain is non-trivial. Inspired by recent progress in symbolic computation of discontinuous Galerkin finite element…
A new method for interface tracking is presented. The interface representation, based on domain decomposition, provides the interface location explicitly, yet is Eulerian. This allows for well established finite difference methods on…
This work proposes a novel variational approximation of partial differential equations on moving geometries determined by explicit boundary representations. The benefits of the proposed formulation are the ability to handle large…
The boundary integral method is an efficient approach for solving time-harmonic acoustic obstacle scattering problems. The main computational task is the evaluation of an oscillatory boundary integral at each discretization point of the…
We develop a numerical method for solving a free boundary problem which describes shape relaxation, by surface tension, of a long and thin bubble of an inviscid fluid trapped inside a viscous fluid in a Hele-Shaw cell. 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 Immersed Boundary method has evolved into one of the most useful computational methods in studying fluid structure interaction. On the other hand, the Immersed Boundary method is also known to suffer from a severe timestep stability…
We present a new analytical and numerical framework for solution of Partial Differential Equations (PDEs) that is based on an exact transformation that moves the boundary constraints into the dynamics of the corresponding governing…
Fluid-structure systems occur in a range of scientific and engineering applications. The immersed boundary(IB) method is a widely recognized and effective modeling paradigm for simulating fluid-structure interaction(FSI) in such systems,…
The Mullins-Sekerka problem is numerically solved in $\mathbb{R}^2$ with the aid of the charge simulation method. This is an expansion of the numerical scheme by which Sakakibara and Yazaki computed the Hele-Shaw flow. We investigate a…
We propose an efficient numerical method for the simulation of multi-phase flows with moving contact lines in three dimensions. The mathematical model consists of the incompressible Navier-Stokes equations for the two immiscible fluids with…
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a…
The Immersed Interface Method is employed to solve the time-varying electric field equations around a three-dimensional vesicle. To achieve second-order accuracy the implicit jump conditions for the electric potential, up to the second…
We develop an immersed boundary (IB) method for modeling flows around fixed or moving rigid bodies that is suitable for a broad range of Reynolds numbers, including steady Stokes flow. The spatio-temporal discretization of the fluid…
This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…
This paper is concerned with the application of time domain boundary integral methods(TDBIMs) to a non-stationary boundary value problem for the thermo-elasto-dynamic equations, based on the Lubich approach via the Laplace transform.…
We present an enhanced immersed interface method for simulating incompressible fluid flows in thin gaps between closely spaced immersed boundaries. This regime, common in engineered structures such as including tribological interfaces and…
This paper investigates a nonlocal boundary value problem for a multi-parametric integral-differential equation involving the Caputo-Prabhakar type operator in a bounded rectangular domain. The nonlocal conditions are given as partial…