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There is a growing interest in investigating numerical approximations of the water wave equation in recent years, whereas the lack of rigorous analysis of its time discretization inhibits the design of more efficient algorithms. In this…

Numerical Analysis · Mathematics 2017-12-14 Lei Li , Jian-Guo Liu , Zibu Liu , Yi Yang , Zhennan Zhou

We present a three-dimensional (3D) partitioned aeroelastic formulation for a flexible multibody system interacting with incompressible turbulent fluid flow. While the incompressible Navier-Stokes system is discretized using a stabilized…

Fluid Dynamics · Physics 2020-11-03 Vaibhav Joshi , Rajeev K. Jaiman , Carl Ollivier-Gooch

We study the construction and convergence of semi-explicit and iterative decoupling schemes for an elliptic-parabolic problem using higher-order Runge-Kutta methods. For the semi-explicit schemes, which are constructed using a nearby delay…

Numerical Analysis · Mathematics 2026-05-22 Robert Altmann , Abdullah Mujahid , Benjamin Unger

Fluid simulations are often performed using the incompressible Navier-Stokes equations (INSE), leading to sparse linear systems which are difficult to solve efficiently in parallel. Recently, kinetic methods based on the…

Graphics · Computer Science 2021-01-29 Yixin Chen , Wei Li , Rui Fan , Xiaopei Liu

Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were proposed and analyzed in 4. These specially designed methods use reduced precision for the implicit computations and full…

Numerical Analysis · Mathematics 2022-12-23 Ben Burnett , Sigal Gottlieb , Zachary J. Grant

We develop a novel and efficient iterative scheme for solving incompressible steady Navier-Stokes equations. The method is an adaptation of the Incremental Viscosity Splitting approximation for unsteady flows to steady equations. At each…

Numerical Analysis · Mathematics 2026-05-07 Aziz Takhirov , Driss Yakoubi

This paper presents a characteristic-based flux partitioning for the semi-implicit time integration of atmospheric flows. Nonhydrostatic models require the solution of the compressible Euler equations. The acoustic time-scale is…

Computational Engineering, Finance, and Science · Computer Science 2018-03-21 Debojyoti Ghosh , Emil M. Constantinescu

In this work we consider a mixed precision approach to accelerate the implemetation of multi-stage methods. We show that Runge-Kutta methods can be designed so that certain costly intermediate computations can be performed as a…

Numerical Analysis · Mathematics 2020-12-25 Zachary J. Grant

Radiation hydrodynamics are a challenging multiscale and multiphysics set of equations. To capture the relevant physics of interest, one typically must time step on the hydrodynamics timescale, making explicit integration the obvious…

Numerical Analysis · Mathematics 2024-08-14 Ben S. Southworth , HyeongKae Park , Svetlana Tokareva , Marc Charest

This paper illuminates the derivation, the applicability, and the efficiency of the Multiplicative Runge-Kutta Method, derived in the frame- work of geometric multiplicative calculus. The removal of the restrictions of geometric…

Numerical Analysis · Mathematics 2019-02-20 Mustafa Riza , Hatice Aktöre

In the present paper, a fluid-particle coupling method is directly derived from the Navier-Stokes equations (NSE) by applying the concept of volume-filtering, yielding a physically consistent methodology to incorporate solid wall boundary…

Fluid Dynamics · Physics 2024-10-17 Max Hausmann , Hani Elmestikawy , Berend van Wachem

We prove the existence of martingale solutions to a stochastic fluid-structure interaction problem involving a viscous, incompressible fluid flow, modeled by the Navier-Stokes equations, through a deformable elastic tube modeled by…

Analysis of PDEs · Mathematics 2024-02-22 Krutika Tawri

Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…

Numerical Analysis · Mathematics 2025-06-24 Robert C. Kirby , John D. Stephens

A novel optimization procedure for the generation of stability polynomials of stabilized explicit Runge-Kutta methods is devised. Intended for semidiscretizations of hyperbolic partial differential equations, the herein developed approach…

Numerical Analysis · Mathematics 2024-03-19 Daniel Doehring , Gregor J. Gassner , Manuel Torrilhon

We present a numerical formulation for the solution of non-isothermal, compressible, Navier-Stokes equations with thermal fluctuations to describe mesoscale transport phenomena in multispecies fluid mixtures. The novelty of our numerical…

A highly efficient gas-kinetic scheme with fourth-order accuracy in both space and time is developed for the Navier-Stokes equations on triangular meshes. The scheme combines an efficient correction procedure via reconstruction (CPR)…

Numerical Analysis · Mathematics 2020-10-20 Chao Zhang , Qibing Li , Z. J. Wang , Jiequan Li , Song Fu

Mixed-precision methods combine low and high precision arithmetics to exploit low precision computational speed and high precision accuracy. Large ODE systems that contain many heterogeneous interactions lead to a high computational cost…

Numerical Analysis · Mathematics 2026-05-25 Mouhamad Al-Sayed , Samuel Bernard , Arsène Marzorati , Jonathan Rouzaud-Cornabas

We present mode-coupling theory (MCT) results for densely packed hard-sphere fluids confined between two parallel walls and compare them quantitatively to computer simulations. The numerical solution of MCT is calculated for the first time…

Soft Condensed Matter · Physics 2023-05-10 Gerhard Jung , Thomas Franosch

A component-splitting method is proposed to improve convergence characteristics for implicit time integration of compressible multicomponent reactive flows. The characteristic decomposition of flux jacobian of multicomponent Navier-Stokes…

Numerical Analysis · Mathematics 2024-03-07 Jingchao Zhang , Jinsheng Cai , Shucheng Pan

We construct solutions to the Navier-Stokes equations on $\mathbf{R}^2$ with an arbitrary number of stagnation points which merge and split along trajectories that can be prescribed freely, up to a small deformation.

Analysis of PDEs · Mathematics 2025-10-02 Isidro Benaroya , Alberto Enciso , Daniel Peralta-Salas