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A high order finite difference method is proposed for unstructured meshes to simulate compressible inviscid/viscous flows with/without discontinuities. In this method, based on the strong form equation, the divergence of the flux on each…

Numerical Analysis · Mathematics 2021-09-08 Zeyuan Zhou , Mei-Yuan Zhen , Kun Qu , Jin-Sheng Cai

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

Among the algorithms that are likely to play a major role in future exascale computing, the fast multipole method (FMM) appears as a rising star. Our previous recent work showed scaling of an FMM on GPU clusters, with problem sizes in the…

Numerical Analysis · Computer Science 2012-10-30 Rio Yokota , Lorena Barba

The capability to incorporate moving geometric features within models for complex simulations is a common requirement in many fields. Fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines,…

Numerical Analysis · Mathematics 2021-04-27 Edward Laughton , Gavin Tabor , David Moxey

A comprehensive scheme for the spatial discretisation of continuity equation, momentum advection and normal and shear stresses at the fluid interfaces is presented for numerically simulating the incompressible two phase flows based on the…

Fluid Dynamics · Physics 2014-08-11 Jun-De Li

Artificial intelligence-based three-dimensional(3D) fluid modeling has gained significant attention in recent years. However, the accuracy of such models is often limited by the processing of irregular flow data. In order to bolster the…

Fluid Dynamics · Physics 2023-07-17 Xin Li , Zhiwen Deng , Rui Feng , Ziyang Liu , Renkun Han , Hongsheng Liu , Gang Chen

Video frame interpolation (VFI) is the task that synthesizes the intermediate frame given two consecutive frames. Most of the previous studies have focused on appropriate frame warping operations and refinement modules for the warped…

Computer Vision and Pattern Recognition · Computer Science 2023-03-24 Sangjin Lee , Hyeongmin Lee , Chajin Shin , Hanbin Son , Sangyoun Lee

Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…

Numerical Analysis · Mathematics 2024-02-27 Jennifer E. Fromm , Nils Wunsch , Kurt Maute , John A. Evans , Jiun-Shyan Chen

Purpose: This study aims to assess the robustness and accuracy of the face-centred finite volume (FCFV) method for the simulation of compressible laminar flows in different regimes, using numerical benchmarks. Design/methodology/approach:…

Fluid Dynamics · Physics 2023-08-01 Jordi Vila-Pérez , Matteo Giacomini , Antonio Huerta

In this study, a fast multipole method (FMM) is used to decrease the computational time of a fully-coupled poroelastic hydraulic fracture model with a controllable effect on its accuracy. The hydraulic fracture model is based on the…

Numerical Analysis · Computer Science 2019-10-23 Ali Rezaei , Fahd Siddiqui , Giorgio Bornia , Mohamed Y. Soliman

The paper is concerned with an adjoint complement to the Volume-of-Fluid (VoF) method for immiscible two-phase flows, e.g. air and water, which is widely used in marine engineering due to its computational efficiency. The particular…

Fluid Dynamics · Physics 2021-06-02 Niklas Kühl , Jörn Kröger , Martin Siebenborn , Michael Hinze , Thomas Rung

Prevailing video frame interpolation algorithms, that generate the intermediate frames from consecutive inputs, typically rely on complex model architectures with heavy parameters or large delay, hindering them from diverse real-time…

Computer Vision and Pattern Recognition · Computer Science 2022-05-31 Lingtong Kong , Boyuan Jiang , Donghao Luo , Wenqing Chu , Xiaoming Huang , Ying Tai , Chengjie Wang , Jie Yang

In CAGD the design of a surface that interpolates an arbitrary quadrilateral mesh is definitely a challenging task. The basic requirement is to satisfy both criteria concerning the regularity of the surface and aesthetic concepts. With…

Numerical Analysis · Mathematics 2016-01-08 Michele Antonelli , Carolina Vittoria Beccari , Giulio Casciola

The stability of most surface-tension-driven interfacial flow simulations is governed by the capillary time-step constraint. This concerns particularly small-scale flows and, more generally, highly-resolved liquid-gas simulations with…

Fluid Dynamics · Physics 2024-10-24 Romain Janodet , Berend van Wachem , Fabian Denner

A volume penalization-based immersed boundary technique is developed and thoroughly validated for fluid flow problems, specifically flow over bluff bodies. The proposed algorithm has been implemented in an Open Source Field Operation and…

Fluid Dynamics · Physics 2023-09-19 Prashant Kumar , Vivek Kumar , Di Chen , Yosuke Hasegawa

Recent progress in large-scale text-to-video (T2V) and image-to-video (I2V) diffusion models has greatly enhanced video generation, especially in terms of keyframe interpolation. However, current image-to-video diffusion models, while…

Computer Vision and Pattern Recognition · Computer Science 2025-03-04 Serin Yang , Taesung Kwon , Jong Chul Ye

The multigrid algorithm is a multilevel approach to accelerate the numerical solution of discretized differential equations in physical problems involving long-range interactions. Multiresolution analysis of wavelet theory provides an…

Computational Physics · Physics 2007-05-23 D. Yesilleten , T. A. Arias

Since viscoelastic two-phase flows arise in various industrial and natural processes, developing accurate and efficient software for their detailed numerical simulation is a highly relevant and challenging research task. We present a…

Fluid Dynamics · Physics 2025-01-08 Matthias Niethammer , Muhammad Hassan Asghar , Tomislav Maric , Dieter Bothe

A robust finite volume method for viscoelastic flow analysis on general unstructured meshes is developed. It is built upon a general-purpose stabilization framework for high Weissenberg number flows. The numerical framework provides full…

Fluid Dynamics · Physics 2020-12-08 Matthias Niethammer , Holger Marschall , Christian Kunkelmann , Dieter Bothe

In this work, we introduce new second-order schemes for one- and two-dimensional hyperbolic systems of conservation laws. Following an approach recently proposed in [{\sc R. Abgrall}, Commun. Appl. Math. Comput., 5 (2023), pp. 370--402], we…

Numerical Analysis · Mathematics 2025-12-24 Rémi Abgrall , Alina Chertock , Alexander Kurganov , Lorenzo Micalizzi
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