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This article presents a Galerkin projection-based reduced-order modelling (ROM) approach for segregated fluid-structure interaction (FSI) problems, formulated within an Arbitrary Lagrangian Eulerian (ALE) framework at low Reynolds numbers…

Numerical Analysis · Mathematics 2025-07-24 Valentin Nkana Ngan , Giovanni Stabile , Andrea Mola , Gianluigi Rozza

We introduce a new family of high order accurate semi-implicit schemes for the solution of non-linear hyperbolic partial differential equations on unstructured polygonal meshes. The time discretization is based on a splitting between…

Numerical Analysis · Mathematics 2023-09-11 Walter Boscheri , Andrea Chiozzi , Michele Giuliano Carlino , Giulia Bertaglia

This paper presents a quasi-monolithic localized high-order arbitrary Lagrangian-Eulerian (qMLH-ALE) finite element method for multi-scale fluid-structure interaction (FSI) in microfluidic systems. The fluid momentum, the incompressible…

Numerical Analysis · Mathematics 2026-05-26 Lingyue Shen , Qi Xin , Yan Chen , Jiarui Han , Yumiao Zhang , Jinchao Xu , Shihua Gong

The incompressible Euler equations are an important model system in computational fluid dynamics. Fast high-order methods for the solution of this time-dependent system of partial differential equations are of particular interest: due to…

Numerical Analysis · Mathematics 2024-10-15 Eike Hermann Müller

The residual-based variational multiscale (VMS) formulation has achieved remarkable success in large-eddy simulation of turbulent flows. However, its temporal discretization has largely remained limited to second-order implicit schemes. The…

Fluid Dynamics · Physics 2025-12-09 Yujie Sun , Chi Ding , Ju Liu

We present a partitioned Model Order Reduction method for multiphysics problems, that is based on a semi-implicit treatment of the coupling conditions, and on a projection scheme. The proposed Reduced Order Method is based on the Proper…

Numerical Analysis · Mathematics 2023-08-08 Monica Nonino , Francesco Ballarin , Gianluigi Rozza , Yvon Maday

The goal of this paper is to develop 2nd order Implicit-Explicit Runge-Kutta (IMEX-RK) finite volume (FV) schemes for solving 1d parabolic PDEs for option pricing, with possible nonlinearities in the source and advection terms. The spatial…

We introduce optimization-based full-order and reduced-order formulations of fluid structure interaction problems. We study the flow of an incompressible Newtonian fluid which interacts with an elastic body: we consider an arbitrary…

Numerical Analysis · Mathematics 2024-12-30 Tommaso Taddei , Xuejun Xu , Lei Zhang

Segregated Runge-Kutta (SRK) schemes are time integration methods for the incompressible Navier-Stokes equations. In this approach, convection and diffusion can be independently treated either explicitly or implicitly, which in particular…

Numerical Analysis · Mathematics 2025-06-12 Pavel Bakhvalov

In this paper, a type of novel projection-based, time-segmented reduced order model (ROM) is proposed for dynamic fluid-structure interaction (FSI) problems based upon the arbitrary Lagrangian--Eulerian (ALE)-finite element method (FEM) in…

Computational Engineering, Finance, and Science · Computer Science 2024-02-16 Qijia Zhai , Shiquan Zhang , Pengtao Sun , Xiaoping Xie

Isospectral Runge-Kutta methods are well-suited for the numerical solution of isospectral systems such as the rigid body and the Toda lattice. More recently, these integrators have been applied to geophysical fluid models, where their…

Numerical Analysis · Mathematics 2025-06-10 Clauson Carvalho da Silva , Christian Lessig , Carlos Tomei

A novel class of high-order linearly implicit energy-preserving integrating factor Runge-Kutta methods are proposed for the nonlinear Schr\"odinger equation. Based on the idea of the scalar auxiliary variable approach, the original equation…

Numerical Analysis · Mathematics 2021-12-07 Chaolong Jiang , Jin Cui , Xu Qian , Songhe Song

When evolving in time the solution of a hyperbolic partial differential equation, it is often desirable to use high order strong stability preserving (SSP) time discretizations. These time discretizations preserve the monotonicity…

Numerical Analysis · Mathematics 2017-08-02 Sidafa Conde , Sigal Gottlieb , Zachary J. Grant , John N. Shadid

The present works is focused on studying bifurcating solutions in compressible fluid dynamics. On one side, the physics of the problem is thoroughly investigated using high-fidelity simulations of the compressible Navier-Stokes equations…

Numerical Analysis · Mathematics 2022-12-21 Niccolò Tonicello , Andrea Lario , Gianluigi Rozza , Gianmarco Mengaldo

One of main obstacles in verifying the energy dissipation laws of implicit-explicit Runge-Kutta (IERK) methods for phase field equations is to establish the uniform boundedness of stage solutions without the global Lipschitz continuity…

Numerical Analysis · Mathematics 2024-12-11 Hong-lin Liao , Tao Tang , Xuping Wang , Tao Zhou

We propose a practical implementation of high-order fully implicit Runge-Kutta(IRK) methods in a multiple precision floating-point environment. Although implementations based on IRK methods in an IEEE754 double precision environment have…

Numerical Analysis · Mathematics 2013-06-18 Tomonori Kouya

This work introduces a new class of Runge-Kutta methods for solving nonlinearly partitioned initial value problems. These new methods, named nonlinearly partitioned Runge-Kutta (NPRK), generalize existing additive and component-partitioned…

Numerical Analysis · Mathematics 2025-04-07 Tommaso Buvoli , Ben S. Southworth

The effects of kinetic-energy preservation errors due to Runge-Kutta (RK) temporal integrators have been analyzed for the case of large-eddy simulations of incompressible turbulent channel flow. Simulations have been run using the…

Fluid Dynamics · Physics 2024-09-16 Marco Artiano , Carlo De Michele , Francesco Capuano , Gennaro Coppola

Non-intrusive model reduction is a promising solution to system dynamics prediction, especially in cases where data are collected from experimental campaigns or proprietary software simulations. In this work, we present a method for…

Fluid Dynamics · Physics 2024-04-04 Leonidas Gkimisis , Thomas Richter , Peter Benner

The context of this work is the development of first order total variation diminishing (TVD) implicit-explicit (IMEX) Runge-Kutta (RK) schemes as a basis of a Multidimensional Optimal Order detection (MOOD) approach to approximate the…

Numerical Analysis · Mathematics 2025-01-08 Victor Michel-Dansac , Andrea Thomann