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We investigate the fluid-poroelastic structure interaction problem in a moving domain, governed by Navier-Stokes-Biot (NSBiot) system. First, we propose a fully parallelizable, loosely coupled scheme to solve the coupled system. At each…

Numerical Analysis · Mathematics 2024-09-25 Shihan Guo , Yizhong Sun , Yifan Wang , Xiaohe Yue , Haibiao Zheng

In this paper, we propose a Runge-Kutta (RK) central discontinuous Galerkin (CDG) gas-kinetic BGK method for the Navier-Stokes equations. The proposed method is based on the CDG method defined on two sets of overlapping meshes to avoid…

Numerical Analysis · Mathematics 2015-06-18 Tan Ren , Jun Hu , Tao Xiong , Jing-Mei Qiu

We present a general simulation approach for fluid-solid interactions based on the fully-Eulerian Reference Map Technique (RMT). The approach permits the modeling of one or more finitely-deformable continuum solid bodies interacting with a…

Fluid Dynamics · Physics 2018-10-09 Chris H. Rycroft , Chen-Hung Wu , Yue Yu , Ken Kamrin

In simulating physical systems, conservation of the total energy is often essential, especially when energy conversion between different forms of energy occurs frequently. Recently, a new fourth order energy-preserving integrator named MB4…

Numerical Analysis · Mathematics 2020-03-11 Tsubasa Sakai , Shuhei Kudo , Hiroto Imachi , Yuto Miyatake , Takeo Hoshi , Yusaku Yamamoto

A new approach to the construction of difference schemes of any order for the many-body problem that preserves all its algebraic integrals is proposed. We introduced additional variables, namely, distances and reciprocal distances between…

Numerical Analysis · Mathematics 2020-07-03 Vladimir Gerdt , Mikhail Malykh , Leonid Sevastianov , Yu Ying

A space-time fully adaptive multiresolution method for evolutionary non-linear partial differential equations is presented introducing an improved local time-stepping method. The space discretisation is based on classical finite volumes,…

Numerical Analysis · Mathematics 2019-05-22 Müller Moreira Lopes , Margarete Oliveira Domingues , Kai Schneider , Odim Mendes

Many practical problems can be described by second-order system $\ddot{q}=-M\nabla U(q)$, in which people give special emphasis to some invariants with explicit physical meaning, such as energy, momentum, angular momentum, etc. However,…

Numerical Analysis · Mathematics 2025-07-25 Wensheng Tang

Simulation of complex dynamical systems arising in many applications is computationally challenging due to their size and complexity. Model order reduction, machine learning, and other types of surrogate modeling techniques offer cheaper…

Numerical Analysis · Mathematics 2026-02-11 Steven Roberts , Andrey A Popov , Arash Sarshar , Adrian Sandu

We investigate a time-periodic fully three-dimensional fluid-structure interaction system in which the Navier-Stokes equations for an incompressible viscous fluid are coupled with a multilayered elastic structure composed of a damped thin…

Analysis of PDEs · Mathematics 2026-03-24 Felix Brandt , Claudiu Mîndrilă , Arnab Roy

Numerical methods for solving the Navier-Stokes equations for classical (or normal) viscous fluids are well established. This is also the case for the Gross-Pitaevskii equation, governing quantum inviscid flows (or superfluids) in the zero…

Quantum Gases · Physics 2023-05-31 Marc Brachet , Georges Sadaka , Zhentong Zhang , Victor Kalt , Ionut Danaila

In this paper, we present a computationally efficient method for including fluid-solid interactions into direct numerical simulations of the Navier-Stokes equations. This method is found to be as powerful as our earlier formulation [J.…

Fluid Dynamics · Physics 2016-06-22 K. Mahady , S. Afkhami , L. Kondic

In this paper we construct higher-order variational integrators for a class of degenerate systems described by Lagrangians that are linear in velocities. We analyze the geometry underlying such systems and develop the appropriate theory for…

Numerical Analysis · Mathematics 2014-01-31 Tomasz M. Tyranowski , Mathieu Desbrun

Generalized Additive Runge-Kutta schemes have shown to be a suitable tool for solving ordinary differential equations with additively partitioned right-hand sides. This work develops symplectic GARK schemes for additively partitioned…

Numerical Analysis · Mathematics 2023-12-14 Michael Günther , Adrian Sandu , Kevin Schäfers , Antonella Zanna

Understanding turbulence is the key to our comprehension of many natural and technological flow processes. At the heart of this phenomenon lies its intricate multi-scale nature, describing the coupling between different-sized eddies in…

The conservation of mass is common issue with multiphase fluid simulations. In this work a novel projection method is presented which conserves mass both locally and globally. The fluid pressure is augmented with a time-varying component…

Fluid Dynamics · Physics 2016-05-24 David Salac

High-order adaptive time-stepping algorithms are of significant practical value and theoretical interest for accelerating long-time fluid-flow simulations and resolving complex dynamical behaviors. While several high-order implicit-explicit…

Numerical Analysis · Mathematics 2026-05-08 Hong-lin Liao , Xiaoming Wang , Xuping Wang , Cao Wen

This work constructs a new class of multirate schemes based on the recently developed generalized additive Runge-Kutta (GARK) methods (Sandu and Guenther, 2013). Multirate schemes use different step sizes for different components and for…

Numerical Analysis · Computer Science 2013-10-24 Michael Guenther , Adrian Sandu

Most research on preconditioners for time-dependent PDEs has focused on implicit multi-step or diagonally-implicit multi-stage temporal discretizations. In this paper, we consider monolithic multigrid preconditioners for fully-implicit…

Numerical Analysis · Mathematics 2023-02-28 Razan Abu-Labdeh , Scott MacLachlan , Patrick E. Farrell

Traditional time discretization methods use a single timestep for the entire system of interest and can perform poorly when the dynamics of the system exhibits a wide range of time scales. Multirate infinitesimal step (MIS) methods (Knoth…

Numerical Analysis · Mathematics 2022-02-03 Steven Roberts , Arash Sarshar , Adrian Sandu

Typical multispecies compressible Navier-Stokes computations employ conservative equations for mass fraction transport. Upwind discretisations of these governing equations produce spurious pressure oscillations at diffuse contact surfaces…

Computational Physics · Physics 2018-06-28 Ben Thornber , Michael Groom , David Youngs