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We extend the shifted boundary method (SBM) to the simulation of incompressible fluid flow using immersed octree meshes. Previous work on SBM for fluid flow primarily utilized two- or three-dimensional unstructured tetrahedral grids.…

The widespread adoption of on-board volumetric imaging in cancer radiotherapy has stimulated research efforts to develop online adaptive radiotherapy techniques to handle the inter-fraction variation of the patient's geometry. Such efforts…

Medical Physics · Physics 2015-05-14 Chunhua Men , Xuejun Gu , Dongju Choi , Amitava Majumdar , Ziyi Zheng , Klaus Mueller , Steve B. Jiang

In this paper, we describe a numerical algorithm for the self-consistent simulations of surface water and sediment dynamics. The method is based on the original Lagrangian-Eulerian CSPH-TVD approach for solving the Saint-Venant and Exner…

Numerical Analysis · Mathematics 2021-03-30 Sergey Khrapov , Alexander Khoperskov

We present an algorithm specifically tailored for solving kinetic equations onto GPUs. The efficiency of the algorithm is demonstrated by solving the one-dimensional shock wave structure problem and a two-dimensional low Mach number driven…

Computational Physics · Physics 2012-05-03 Aldo Frezzotti , Gian Pietro Ghiroldi , Livio Gibelli

The Lattice Boltzmann method (LBM) for solving fluid flow is naturally well suited to an efficient implementation for massively parallel computing, due to the prevalence of local operations in the algorithm. This paper presents and analyses…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-01-04 Mark Mawson , Alistair Revell

Despite decades of advancements, the simulation of fluids remains one of the most challenging areas of in scientific computing. Supported by the necessity of gradient information in deep learning, differentiable simulators have emerged as…

Machine Learning · Computer Science 2025-10-21 Aleksandra Franz , Hao Wei , Luca Guastoni , Nils Thuerey

Hydrodynamics calculations have been successfully used in studies of the bulk properties of the Quark-Gluon Plasma, particularly of elliptic flow and shear viscosity. However, there are areas (for instance event-by-event simulations for…

An alternating direction method of multipliers (ADMM) solver is described for optimal resource allocation problems with separable convex quadratic costs and constraints and linear coupling constraints. We describe a parallel implementation…

Optimization and Control · Mathematics 2019-07-09 Zawar Qureshi , Sebastian East , Mark Cannon

Oscillator-based Ising machines (OIMs) and oscillator-based Potts machines (OPMs) have emerged as promising hardware accelerators for solving NP-hard combinatorial optimization problems by leveraging the phase dynamics of coupled…

Hardware Architecture · Computer Science 2025-05-29 Yilmaz Ege Gonul , Ceyhun Efe Kayan , Ilknur Mustafazade , Nagarajan Kandasamy , Baris Taskin

The simulation of heat flow through heterogeneous material is important for the design of structural and electronic components. Classical analytical solutions to the heat equation PDE are not known for many such domains, even those having…

Numerical Analysis · Mathematics 2019-05-21 Andrew Loeb , Christopher Earls

Inverse problems in fluid dynamics are ubiquitous in science and engineering, with applications ranging from electronic cooling system design to ocean modeling. We propose a general and robust approach for solving inverse problems in the…

Numerical Analysis · Mathematics 2020-11-20 Tiffany Fan , Kailai Xu , Jay Pathak , Eric Darve

Fluid mechanics is a fundamental field in engineering and science. Solving the Navier-Stokes equation (NSE) is critical for understanding the behavior of fluids. However, the NSE is a complex partial differential equation that is difficult…

Computational Physics · Physics 2023-04-10 Ayoub Farkane , Mounir Ghogho , Mustapha Oudani , Mohamed Boutayeb

We present a matrix-free flow solver for high-order finite element discretizations of the incompressible Navier-Stokes and Stokes equations with GPU acceleration. For high polynomial degrees, assembling the matrix for the linear systems…

Numerical Analysis · Mathematics 2020-04-21 Michael Franco , Jean-Sylvain Camier , Julian Andrej , Will Pazner

We introduce CaLES, a GPU-accelerated finite-difference solver designed for large-eddy simulations (LES) of incompressible wall-bounded flows in massively parallel environments. Built upon the existing direct numerical simulation (DNS)…

Fluid Dynamics · Physics 2024-11-18 Maochao Xiao , Alessandro Ceci , Pedro Costa , Johan Larsson , Sergio Pirozzoli

In computational fluid dynamics, the demand for increasingly multidisciplinary reliable simulations, for both analysis and design optimization purposes, requires transformational advances in individual components of future solvers. At the…

Computational fluid dynamics is both a thriving research field and a key tool for advanced industry applications. The central challenge is to simulate turbulent flows in complex geometries, a compute-power intensive task due to the large…

We present Aquarium, a differentiable fluid-structure interaction solver for robotics that offers stable simulation, accurately coupled fluid-robot physics in two dimensions, and full differentiability with respect to fluid and robot states…

Robotics · Computer Science 2023-03-09 Jeong Hun Lee , Mike Y. Michelis , Robert Katzschmann , Zachary Manchester

Numerical simulation is indispensable in industrial design processes. It can replace expensive experiments and even reduce the need for prototypes. While products designed with the aid of numerical simulation undergo continuous improvement,…

Numerical Analysis · Mathematics 2020-06-04 Henning Wessels , Christian Weißenfels , Peter Wriggers

Conventional mathematical models for simulating incompressible fluid flow problems are based on the Navier-Stokes equations expressed in terms of pressure and velocity. In this context, pressure-velocity coupling is a key issue, and…

Mathematical Physics · Physics 2025-06-06 Ricardo Costa , Stéphane Clain , Gaspar J. Machado , João M. Nóbrega

In this paper, a new progressive mesh algorithm is introduced in order to perform fast physical simulations by the use of a lattice Boltzmann method (LBM) on a single-node multi-GPU architecture. This algorithm is able to mesh automatically…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-10-14 Julien Duchateau , François Rousselle , Nicolas Maquignon , Gilles Roussel , Christophe Renaud
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