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We present an integral equation-based method for the numerical solution of two-point boundary value systems. Special care is devoted to the mathematical formulation, namely the choice of the background Green's function that leads to a…

Numerical Analysis · Mathematics 2025-10-09 Tianze Zhang , Yixuan Ma , Jun Wang

In this paper, exploiting variational methods, the existence of multiple weak solutions for a class of elliptic Navier boundary problems involving the $p$-biharmonic operator is investigated. Moreover, a concrete example of an application…

Analysis of PDEs · Mathematics 2016-08-29 Giovanni Molica Bisci , Dušan Repovš

We introduce and analyze various Regularized Combined Field Integral Equations (CFIER) formulations of time-harmonic Navier equations in media with piece-wise constant material properties. These formulations can be derived systematically…

Numerical Analysis · Mathematics 2022-04-21 Victor Dominguez , Catalin Turc

This paper is concerned with the cavity scattering problem in an infinite thin plate, where the out-of-plane displacement is governed by the two-dimensional biharmonic wave equation. Based on an operator splitting, the scattering problem is…

Numerical Analysis · Mathematics 2023-01-25 Heping Dong , Peijun Li

In this paper we consider a class of fourth order nonlinear integro-differential equations with Navier boundary conditions. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…

Numerical Analysis · Mathematics 2020-12-22 Dang Quang A , Dang Quang Long

In conventional fluid mechanics, the chemical composition and thermodynamic state of a fluid-solid interface are not considered when establishing velocity-field boundary conditions. As a consequence, fluid simulations are usually not able…

We present an improved method for computing incompressible viscous flow around suspended rigid particles using a fixed and uniform computational grid. The main idea is to incorporate Peskin's regularized delta function approach [Acta…

Fluid Dynamics · Physics 2018-09-24 Markus Uhlmann

We evaluate an efficient overset grid method for two-dimensional and three-dimensional particulate flows for small numbers of particles at finite Reynolds number. The rigid particles are discretised using moving overset grids overlaid on a…

Computational Physics · Physics 2017-05-24 A. R. Koblitz , S. Lovett , N. Nikiforakis , W. D. Henshaw

We study a moving boundary value problem consisting of a viscous incompressible fluid moving and interacting with a nonlinear elastic solid shell. The fluid motion is governed by the Navier-Stokes equations, while the shell is modeled by…

Analysis of PDEs · Mathematics 2007-05-23 C. H. Arthur Cheng , Daniel Coutand , Steve Shkoller

Phase separation of binary fluids quenched by contact with cold external walls is considered. Navier-Stokes, convection-diffusion, and energy equations are solved by lattice Boltzmann method coupled with finite-difference schemes. At high…

Soft Condensed Matter · Physics 2015-05-20 G. Gonnella , A. Lamura , A. Piscitelli , A. Tiribocchi

An approximate solution to the two dimensional Navier Stokes equation with periodic boundary conditions is obtained by representing the x any y components of fluid velocity with complex Fourier basis vectors. The chosen space of basis…

Dynamical Systems · Mathematics 2016-07-05 Logan K. Kuiper

We consider a computational model for complex-fluid-solid interaction based on a diffuse-interface model for the complex fluid and a hyperelastic-material model for the solid. The diffuse-interface complex-fluid model is described by the…

Numerical Analysis · Mathematics 2015-10-09 E. H. van Brummelen , M. Shokrpour-Roudbari , G. J. van Zwieten

We study the barotropic compressible Navier-Stokes equations with Navier-type boundary condition in a two-dimensional simply connected bounded domain with $C^{\infty}$ boundary $\partial\Omega.$ By some new estimates on the boundary related…

Analysis of PDEs · Mathematics 2021-04-22 Yuebo Cao

An initial boundary value problem for one-dimensional hyperbolic compressible Navier-Stokes equations is investigated. After transforming the system into Lagrangian coordinate, the resulting system possesses a structure with uniform…

Analysis of PDEs · Mathematics 2025-08-05 Yuxi Hu , Yachun Li

A new simulation method for solving fluid-structure coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A volume-of-fluid formulation (Hirt and…

Computational Physics · Physics 2015-05-20 Kazuyasu Sugiyama , Satoshi Ii , Shintaro Takeuchi , Shu Takagi , Yoichiro Matsumoto

A second-order accurate kernel-free boundary integral method is presented for Stokes and Navier boundary value problems on three-dimensional irregular domains. It solves equations in the framework of boundary integral equations, whose…

Numerical Analysis · Mathematics 2023-06-28 Zhongshu Zhao , Haixia Dong , Wenjun Ying

We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…

Numerical Analysis · Mathematics 2024-11-19 R. Drebotiy , H. Shynkarenko

The problem of choice of boundary conditions are discussed for the case of numerical integration of the shallow water equations on a substantially irregular relief. In modeling of unsteady surface water flows has a dynamic boundary…

Fluid Dynamics · Physics 2017-09-29 T. A. Dyakonova , S. S. Khrapov , A. V. Khoperskov

We study a nonlinear, unsteady, moving boundary, fluid-structure (FSI) problem in which the structure is composed of two layers: a thin layer which is in contact with the fluid, and a thick layer which sits on top of the thin structural…

Analysis of PDEs · Mathematics 2013-05-24 Boris Muha , Suncica Canic

We consider the well-posedness and a priori error estimates of a 3d FEM-BEM coupling method for fluid-structure interaction in the time domain. For an elastic body immersed in a fluid, the exterior linear wave equation for the fluid is…

Numerical Analysis · Mathematics 2020-08-12 Heiko Gimperlein , Ceyhun Oezdemir , Ernst P. Stephan