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In this work, we propose a telegraph coupled partial differential equation (TCPDE) based model for image restoration. New framework interpolates between a couple of non-linear telegraph equation and a parabolic equation. Proposed strategy…

Analysis of PDEs · Mathematics 2019-09-12 Sudeb Majee , Subit K. Jain , Rajendra K. Ray , Ananta K. Majee

This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…

Computational Physics · Physics 2021-06-04 Tim Wallis , Philip T. Barton , Nikolaos Nikiforakis

We consider a loosely coupled, non-iterative Robin-Robin coupling method proposed and analyzed in [Numer. Algorithms, 99:921-948, 2025] for a parabolic-parabolic interface problem. We modify the first step of the scheme so that several…

Numerical Analysis · Mathematics 2025-09-11 Erik Burman , Miguel A. Fernandez , Johnny Guzman , Sijing Liu

Hyperbolic systems under nonconservative form arise in numerous applications modeling physical processes, for example from the relaxation of more general equations (e.g. with dissipative terms). This paper reviews an existing class of…

Numerical Analysis · Mathematics 2020-05-14 Adrián Navas-Montilla , Ilhan Özgen-Xian

We prove the existence of finite-energy weak solutions to a regularized three-dimensional fluid-structure interaction (FSI) problem involving an incompressible, viscous, Newtonian fluid and a multilayered poro(visco)elastic structure. The…

Analysis of PDEs · Mathematics 2025-08-21 Felix Brandt , Sunčica Čanić , Boris Muha

In this paper, we construct and analyze a multiscale (finite element) method for parabolic problems with heterogeneous dynamic boundary conditions. As origin, we consider a reformulation of the system in order to decouple the discretization…

Numerical Analysis · Mathematics 2020-09-16 Robert Altmann , Barbara Verfürth

We present a new approach to analyze the validation of weakly nonlinear geometric optics for entropy solutions of nonlinear hyperbolic systems of conservation laws whose eigenvalues are allowed to have constant multiplicity and…

Analysis of PDEs · Mathematics 2012-12-27 Gui-Qiang Chen , Wei Xiang , Yongqian Zhang

We introduce novel approximate systems for dispersive and diffusive-dispersive equations with nonlinear fluxes. For purely dispersive equations, we construct a first-order, strictly hyperbolic approximation. Local well-posedness of smooth…

Analysis of PDEs · Mathematics 2025-12-05 Rahul Barthwal , Firas Dhaouadi , Christian Rohde

We propose a finite volume scheme for a class of nonlinear parabolic equations endowed with non-homogeneous Dirichlet boundary conditions and which admit relative en-tropy functionals. For this kind of models including porous media…

Numerical Analysis · Mathematics 2017-04-21 Francis Filbet , Maxime Herda

We present a strongly-coupled immersed-boundary method for flow-structure interaction problems involving thin deforming bodies. The method is stable for arbitrary choices of solid-to-fluid mass ratios and for large body motions. As with…

Fluid Dynamics · Physics 2016-10-05 Andres Goza , Tim Colonius

We introduce a diffuse interface model describing the evolution of a mixture of two different viscous incompressible fluids of equal density. The main novelty of the present contribution consists in the fact that the effects of temperature…

Analysis of PDEs · Mathematics 2014-01-15 Michela Eleuteri , Elisabetta Rocca , Giulio Schimperna

A novel mathematical model for fiber-reinforced materials is proposed. It is based on a 1-dimensional beam model for the thin fiber structures, a flexible and general 3-dimensional elasticity model for the matrix and an overlapping domain…

Computational Engineering, Finance, and Science · Computer Science 2021-05-12 Ustim Khristenko , Stefan Schuß , Melanie Krüger , Felix Schmidt , Barbara Wohlmuth , Christian Hesch

This work outlines a new multi-physics-compatible immersed rigid body method for Eulerian finite-volume simulations. To achieve this, rigid bodies are represented as a diffuse scalar field and an interface seeding method is employed to…

Computational Physics · Physics 2022-03-15 Tim Wallis , Philip Barton , Nikolaos Nikiforakis

In this work we analyze the stability and convergence properties of a loosely-coupled scheme, called the kinematically coupled scheme, and its extensions for the interaction between an incompressible, viscous fluid and a thin, elastic…

Numerical Analysis · Mathematics 2016-08-30 Martina Bukac , Boris Muha

A novel thermodynamically consistent diffuse interface model is derived for compressible electrolytes with phase transitions. The fluid mixtures may consist of N constituents with the phases liquid and vapor, where both phases may coexist.…

Analysis of PDEs · Mathematics 2014-11-13 Wolfgang Dreyer , Jan Giesselmann , Christiane Kraus

Fluid-particle systems are very common in many natural processes and engineering applications. However, accurately and efficiently modelling fluid-particle systems with complex particle shapes is still a challenging task. Here, we present a…

Fluid Dynamics · Physics 2023-03-22 Pei Zhang , Ling Qiu , S. A. Galindo-Torres , Yilin Chen , A. Scheuermann , Ling Li

We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems that lead to energy and entropy bounded solutions. A step-by-step procedure for general nonlinear hyperbolic problems on…

Numerical Analysis · Mathematics 2024-05-10 Jan Nordström

In this work we analyze the stability and convergence properties of a loosely-coupled scheme, called the kinematically coupled scheme, for interaction between an incompressible viscous fluid and a thin structure. We consider a benchmark…

Numerical Analysis · Mathematics 2014-06-16 Martina Bukac

The Active Flux scheme is a finite volume scheme with additional point values distributed along the cell boundary. It is third order accurate and does not require a Riemann solver. Instead, given a reconstruction, the initial value problem…

Numerical Analysis · Mathematics 2020-11-23 Wasilij Barsukow

We develop a new finite element method for solving planar elasticity problems involving of heterogeneous materials with a mesh not necessarily aligning with the interface of the materials. This method is based on the `broken'…

Numerical Analysis · Mathematics 2015-06-23 Do Y. Kwak , Sangwon Jin , Dae H. Kyeong