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We present the Fluid Transport Accelerated Solver, FluTAS, a scalable GPU code for multiphase flows with thermal effects. The code solves the incompressible Navier-Stokes equation for two-fluid systems, with a direct FFT-based Poisson…

We present a comprehensive validation, performance characterization, and scalability analysis of a hardware-accelerated phase-averaged multiscale solver designed to simulate acoustically driven dilute bubbly suspensions. The carrier fluid…

Fluid Dynamics · Physics 2026-04-24 Diego Vaca-Revelo , Benjamin Wilfong , Spencer H. Bryngelson , Aswin Gnanaskandan

Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting…

Numerical Analysis · Mathematics 2026-02-26 Yating Wang , Zhengya Yang , Wing Tat Leung

We consider the initial-value problem in the $d$-dimensional Euclidean space $\mathbb{R}^d$ $(d \ge 3)$ for the compressible Navier-Stokes-Korteweg equations under the zero sound speed case (namely, $P'(\rho_*)=0$, where $P=P(\rho)$ stands…

Analysis of PDEs · Mathematics 2025-06-03 Takayuki Kobayashi , Ryosuke Nakasato

The stability problem for the 2D Navier-Stokes equations with dissipation in only one direction on $\mathbb R^2$ is not fully understood. This dissipation is in the intermediate regime between the fully dissipative Navier-Stokes and the…

Analysis of PDEs · Mathematics 2026-04-22 Zhibin Wang , Jiahong Wu , Ning Zhu

We implemented the pressure-implicit with splitting of operators (PISO) and semi-implicit method for pressure-linked equations (SIMPLE) solvers of the Navier-Stokes equations on Fermi-class graphics processing units (GPUs) using the CUDA…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-10-01 Tadeusz Tomczak , Katarzyna Zadarnowska , Zbigniew Koza , Maciej Matyka , Łukasz Mirosław

The Reynolds-averaged Navier-Stokes (RANS) equations provide a computationally efficient method for solving fluid flow problems in engineering applications. However, the use of closure models to represent turbulence effects can reduce their…

Fluid Dynamics · Physics 2024-05-02 Oliver Brenner , Justin Plogmann , Pasha Piroozmand , Patrick Jenny

In this paper we consider fully discrete approximations with inf-sup stable mixed finite element methods in space to approximate the Navier-Stokes equations. A continuous downscaling data assimilation algorithm is analyzed in which…

Numerical Analysis · Mathematics 2019-04-15 Bosco García-Archilla , Julia Novo

We introduce, analyze and test a new interpolation operator for use with continuous data assimilation (DA) of evolution equations that are discretized spatially with the finite element method. The interpolant is constructed as an…

Analysis of PDEs · Mathematics 2018-10-09 Leo G. Rebholz , Camille Zerfas

To address the dual challenges of performance portability across heterogeneous hardware and the high usability barriers of conventional computational fluid dynamics (CFD) software, this paper introduces FEALPy.CFD, a high performance,…

Fluid Dynamics · Physics 2026-05-26 Wang Pengxiang , Huang Xianbo , Peng Li , Wei Huayi

The goal of this work is to develop a novel splitting approach for the numerical solution of multiscale problems involving the coupling between Stokes equations and ODE systems, as often encountered in blood flow modeling applications. The…

Numerical Analysis · Mathematics 2018-04-16 Lucia Carichino , Giovanna Guidoboni , Marcela Szopos

A high-order Flux reconstruction implementation of the hyperbolic formulation for the incompressible Navier-Stokes equation is presented. The governing equations employ Chorin's classical artificial compressibility (AC) formulation cast in…

Computational Physics · Physics 2021-06-04 Mohamed M. Kamra , Jabir Al-Salami , Changhong Hu

We construct a decoupled, first-order, fully discrete, and unconditionally energy stable scheme for the Cahn-Hilliard-Navier-Stokes equations. The scheme is divided into two main parts. The first part involves the calculation of the…

Numerical Analysis · Mathematics 2024-08-20 Haijun Gao , Xi Li , Minfu Feng

We present a new hybrid direct/iterative approach to the solution of a special class of saddle point matrices arising from the discretization of the steady incompressible Navier-Stokes equations on an Arakawa C-grid. The two-level method…

Numerical Analysis · Mathematics 2010-06-10 Fred Wubs , Jonas Thies

The lattice Boltzmann method has become a standard for efficiently solving problems in fluid dynamics. While unstructured grids allow for a more efficient geometrical representation of complex boundaries, the lattice Boltzmann methods is…

Inclusion of a term $-\gamma\nabla\nabla\cdot u$, forcing $\nabla\cdot u$ to be pointwise small, is an effective tool for improving mass conservation in discretizations of incompressible flows. However, the added grad-div term couples all…

Numerical Analysis · Mathematics 2022-05-17 William Layton , Shuxian Xu

Partial differential equation solvers are required to solve the Navier-Stokes equations for fluid flow. Recently, algorithms have been proposed to simulate fluid dynamics on quantum computers. Fault-tolerant quantum devices might enable…

Fluid Dynamics · Physics 2025-05-20 Zhixin Song , Robert Deaton , Bryan Gard , Spencer H. Bryngelson

We consider a stabilization method for divergence-conforming B-spline discretizations of the incompressible Navier--Stokes problem wherein jumps in high-order normal derivatives of the velocity field are penalized across interior mesh…

Numerical Analysis · Mathematics 2022-01-28 Guoxiang Grayson Tong , David Kamensky , John A. Evans

This note introduces a novel numerical analysis framework for the incompressible Navier-Stokes equations based on Besov spaces. The key contribution of this note is to establish the stability and convergence of a semi-implicit time-stepping…

Numerical Analysis · Mathematics 2025-09-30 Xinyu Cheng , Zhaonan Luo , Sheng Wang

A numerical method for the two-dimensional, incompressible Navier--Stokes equations in vorticity--streamfunction form is proposed, which employs semi-Lagrangian discretizations for both the advection and diffusion terms, thus achieving…

Numerical Analysis · Mathematics 2018-01-30 Luca Bonaventura , Roberto Ferretti , Lorenzo Rocchi