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A method for modelling non-Newtonian fluids (dilatants and pseudoplastics) by a power law under the Godunov-Peshkov-Romenski model is presented, along with a new numerical scheme for solving this system. The scheme is also modified to solve…

Computational Physics · Physics 2019-05-01 Haran Jackson , Nikos Nikiforakis

We present a new hybrid semi-implicit finite volume / finite element numerical scheme for the solution of incompressible and weakly compressible media. From the continuum mechanics model proposed by Godunov, Peshkov and Romenski (GPR), we…

Numerical Analysis · Mathematics 2025-01-29 Saray Busto , Laura Río-Martín

This paper presents a general and robust method for the fluid-structure interaction of membranes and shells undergoing large displacement and large added-mass effects by coupling an immersed-boundary method with a shell finite-element…

Fluid Dynamics · Physics 2023-08-15 Marin Lauber , Gabriel D. Weymouth , Georges Limbert

A mixed continuous / discontinuous Galerkin scheme is introduced for the simulation of fluid-structure interaction problems in an isogeometric analysis framework. The properties of Non-Uniform Rational B-Spline basis functions are leveraged…

Analysis of PDEs · Mathematics 2026-02-17 Régis Duvigneau

We present a monolithic finite element formulation for (nonlinear) fluid-structure interaction in Eulerian coordinates. For the discretization we employ an unfitted finite element method based on inf-sup stable finite elements. So-called…

Numerical Analysis · Mathematics 2024-02-02 Stefan Frei , Tobias Knoke , Marc C. Steinbach , Anne-Kathrin Wenske , Thomas Wick

In this paper, we present a unified framework to simulate non-Newtonian behaviors. We combine viscous and elasto-plastic stress into a unified particle solver to achieve various non-Newtonian behaviors ranging from fluid-like to solid-like.…

Graphics · Computer Science 2023-12-11 Chunlei Li , Yang Gao , Jiayi He , Tianwei Cheng , Shuai Li , Aimin Hao , Hong Qin

Hydroclimatic processes are characterized by heterogeneous spatiotemporal correlation structures and marginal distributions that can be continuous, mixed-type, discrete or even binary. Simulating exactly such processes can greatly improve…

Methodology · Statistics 2017-07-24 Simon Michael Papalexiou

On the example of two-phase continua experiencing stress induced solid-fluid phase transitions we explore the use of the Euler structure in the formulation of the governing equations. The Euler structure guarantees that solutions of the…

Soft Condensed Matter · Physics 2015-12-02 Ilya Peshkov , Miroslav Grmela , Evgeniy Romenski

We studied numerically the dynamics of colliding rigid bodies in a Newtonian fluid. The finite element method is used to solve the fluid-body interaction and the fluid motion is described in the Arbitrary-Lagrangian-Eulerian framework. To…

This paper proposes a semi-implicit arbitrary Lagrangian-Eulerian (ALE) method for the solution of the unified Godunov-Peshkov-Romenski (GPR) model of continuum mechanics. To handle the curl free involutions arising in the solid limit of…

Numerical Analysis · Mathematics 2025-12-04 Saray Busto

Modern generative models hold great promise for accelerating diverse tasks involving the simulation of physical systems, but they must be adapted to the specific constraints of each domain. Significant progress has been made for…

Machine Learning · Statistics 2025-12-19 Louis Grenioux , Leonardo Galliano , Ludovic Berthier , Giulio Biroli , Marylou Gabrié

We propose an approximate solver for multi-medium Riemann problems with materials described by a family of general Mie-Gr\"uneisen equations of state, which are widely used in practical applications. The solver provides the interface…

Numerical Analysis · Mathematics 2018-04-24 Li Chen , Ruo Li , Chengbao Yao

This work outlines a diffuse interface method for the study of fracture and fragmentation in ductile metals at high strain-rates in Eulerian finite volume simulations. The work is based on an existing diffuse interface method capable of…

Computational Physics · Physics 2022-10-11 Tim Wallis , Philip T. Barton , Nikolaos Nikiforakis

We present an open-source Matlab framework, titled iFluid, for simulating the dynamics of integrable models using the theory of generalized hydrodynamics (GHD). The framework provides an intuitive interface, enabling users to define and…

Statistical Mechanics · Physics 2020-03-18 Frederik S. Møller , Jörg Schmiedmayer

Simulating fluid-granular flows is crucial for understanding natural disasters, industrial processes, and visually realistic phenomena in computer graphics. These systems are challenging to simulate because of the strong nonlinear coupling…

Graphics · Computer Science 2026-03-17 Xingqiao Li , Kui Wu , Haozhe Su , Tianhong Gao , Mengyu Chu , Chenfanfu Jiang , Wei Li , Baoquan Chen

This work presents a unified numerical framework for simulating incompressible flows within the coupled fluid-porous-medium system and involving heat and solute transport and phase-changing process. A complete set of governing equations is…

Fluid Dynamics · Physics 2026-01-28 Rongfu Guo , Yantao Yang

In this work, we consider fluid-structure interaction simulation with nonlinear hyperelastic models in the solid part. We use a partitioned approach to deal with the coupled nonlinear fluid-structure interaction problems. We focus on…

Numerical Analysis · Mathematics 2013-12-20 Ulrich Langer , Huidong Yang

We propose a robust approximate solver for the hydro-elastoplastic solid material, a general constitutive law extensively applied in explosion and high speed impact dynamics, and provide a natural transformation between the fluid and solid…

Numerical Analysis · Mathematics 2019-02-15 Ruo Li , Yanli Wang , Chengbao Yao

In this paper, we consider the flow of an incompressible fluid in a deformable porous solid. We present a mathematical model using the framework offered by the theory of interacting continua. In its most general form, this framework…

Numerical Analysis · Computer Science 2013-02-27 D. Z. Turner , K. B. Nakshatrala , M. J. Martinez

In this work, we consider the solution of fluid-structure interaction problems using a monolithic approach for the coupling between fluid and solid subproblems. The coupling of both equations is realized by means of the arbitrary…

Numerical Analysis · Mathematics 2018-03-09 D. Jodlbauer , U. Langer , T. Wick