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The progress made in accelerating simulations of fluid flow using GPUs, and the challenges that remain, are surveyed. The review first provides an introduction to GPU computing and programming, and discusses various considerations for…

Fluid Dynamics · Physics 2014-02-04 Kyle E Niemeyer , Chih-Jen Sung

Within the domain of Computational Fluid Dynamics, Direct Numerical Simulation (DNS) is used to obtain highly accurate numerical solutions for fluid flows. However, this approach for numerically solving the Navier-Stokes equations is…

Fluid Dynamics · Physics 2021-03-16 Pranshu Pant , Amir Barati Farimani

An in-house large eddy simulation tool is developed in order to reproduce high fidelity results of compressible jet flows. The large eddy simulation formulation is written using the finite difference approach, with an explicit time…

Fluid Dynamics · Physics 2023-01-04 Carlos Junqueira-Junior , Joao Luiz F. Azevedo , Sami Yamouni , William Wolf

In this paper we consider a fully discrete numerical method for the unsteady Navier-Stokes equations on a smooth closed stationary surface in $\mathbb{R}^3$. We use the surface finite element method (SFEM) with a generalized Taylor-Hood…

Numerical Analysis · Mathematics 2025-12-03 Charles M. Elliott , Achilleas Mavrakis

Computational physics simulation can be a powerful tool to accelerate industry deployment of new scientific technologies. However, it must address the challenge of computationally tractable, moderately accurate prediction at large industry…

The ensemble data assimilation of computational fluid dynamics simulations based on the lattice Boltzmann method (LBM) and the local ensemble transform Kalman filter (LETKF) is implemented and optimized on a GPU supercomputer based on…

In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier-Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with…

Numerical Analysis · Mathematics 2022-03-01 Yuhang Wang , Liang Pan

This paper presents a robust, adaptive numerical scheme for simulating high density ratio and high shear multiphase flows on locally refined Cartesian grids that adapt to the evolving interfaces and track regions of high vorticity. The…

Computational Physics · Physics 2019-09-04 Nishant Nangia , Boyce E. Griffith , Neelesh A. Patankar , Amneet Pal Singh Bhalla

Fluid simulation is an important research topic in computer graphics (CG) and animation in video games. Traditional methods based on Navier-Stokes equations are computationally expensive. In this paper, we treat fluid motion as point cloud…

Computer Vision and Pattern Recognition · Computer Science 2025-01-07 Yu Chen , Shuai Zheng , Nianyi Wang , Menglong Jin , Yan Chang

We present a massively parallel, GPU-accelerated implementation of the Bethe-Salpeter equation (BSE) for the calculation of the vertical excitation energies (VEEs) and optical absorption spectra of condensed and molecular systems, starting…

Materials Science · Physics 2024-12-25 Victor Wen-zhe Yu , Yu Jin , Giulia Galli , Marco Govoni

Non Uniform Rational B-spline (NURBS) patches are a standard way to describe complex geometries in Computer Aided Design tools, and have gained a lot of popularity in recent years also for the approximation of partial differential…

Numerical Analysis · Mathematics 2018-07-04 Giuseppe Pitton , Luca Heltai

In the paper we discuss the main features of the software package for numerical simulations of the surface water dynamics. We consider an approximation of the shallow water equations together with the parallel technologies for NVIDIA CUDA…

Computational Engineering, Finance, and Science · Computer Science 2017-05-03 Tatyana Dyakonova , Alexander Khoperskov , Sergey Khrapov

With the recent proliferation of heterogeneous, GPU-accelerated supercomputers, high-order computational fluid dynamics (CFD) simulations of complex, turbulent flows are more accessible than ever. To leverage the computing power of these…

Implementing AI algorithms on event-based embedded devices enables real-time processing of data, minimizes latency, and enhances power efficiency in edge computing. This research explores the deployment of a spiking recurrent neural network…

Machine Learning · Computer Science 2024-09-11 Marzieh Hassanshahi Varposhti , Mahyar Shahsavari , Marcel van Gerven

We present families of space-time finite element methods (STFEMs) for a coupled hyperbolic-parabolic system of poro- or thermoelasticity. Well-posedness of the discrete problems is proved. Higher order approximations inheriting most of the…

Numerical Analysis · Mathematics 2023-03-14 Mathias Anselmann , Markus Bause , Nils Margenberg , Pavel Shamko

Homomorphic Encryption (HE) is an emerging encryption scheme that allows computations to be performed directly on encrypted messages. This property provides promising applications such as privacy-preserving deep learning and cloud…

Cryptography and Security · Computer Science 2021-10-01 Yujia Zhai , Mohannad Ibrahim , Yiqin Qiu , Fabian Boemer , Zizhong Chen , Alexey Titov , Alexander Lyashevsky

We focus on implementing and optimizing a sixth-order finite-difference solver for simulating compressible fluids on a GPU using third-order Runge-Kutta integration. Since graphics processing units perform well in data-parallel tasks, this…

Computational Physics · Physics 2017-07-28 Johannes Pekkilä , Miikka S. Väisälä , Maarit J. Käpylä , Petri J. Käpylä , Omer Anjum

We present the numerical methods, programming methodology, verification, and performance assessment of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit…

Plasma Physics · Physics 2025-07-14 Hariswaran Sitaraman , Nicholas Deak , Taaresh Taneja

Implicit methods and GPU parallelization are two distinct yet powerful strategies for accelerating high-order CFD algorithms. However, few studies have successfully integrated both approaches within high-speed flow solvers. The core…

Numerical Analysis · Mathematics 2025-09-09 Hongyu Liu , Xing Ji , Yuan Fu , Kun Xu

Encrypted AI using fully homomorphic encryption (FHE) provides strong privacy guarantees; but its slow performance has limited practical deployment. Recent works proposed ASICs to accelerate FHE, but require expensive advanced manufacturing…

Cryptography and Security · Computer Science 2025-12-15 Siddharth Jayashankar , Joshua Kim , Michael B. Sullivan , Wenting Zheng , Dimitrios Skarlatos